# Floyd's triangle

Floyd's triangle
You are encouraged to solve this task according to the task description, using any language you may know.

Floyd's triangle   lists the natural numbers in a right triangle aligned to the left where

• the first row is   1     (unity)
• successive rows start towards the left with the next number followed by successive naturals listing one more number than the line above.

The first few lines of a Floyd triangle looks like this:

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```

1. Write a program to generate and display here the first   n   lines of a Floyd triangle.
(Use   n=5   and   n=14   rows).
2. Ensure that when displayed in a mono-space font, the numbers line up in vertical columns as shown and that only one space separates numbers of the last row.

## 11l

Translation of: Python
```F floyd(rowcount)
V rows = [[1]]
L rows.len < rowcount
V n = rows.last.last + 1
rows.append(Array(n .. n + rows.last.len))
R rows

F pfloyd(rows)
V colspace = rows.last.map(n -> String(n).len)
L(row) rows
print(zip(colspace, row).map2((space, n) -> String(n).rjust(space)).join(‘ ’))

pfloyd(floyd(5))
pfloyd(floyd(14))```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## 360 Assembly

 This example is incorrect. Please fix the code and remove this message.Details: The last line should only have one space between values

A very concise coding, an illustration of CISC power of the S/360 operation codes. Also an example of the use of EDMK and EX instructions. For macro usage see Structured Macros .

```*        Floyd's triangle          21/06/2018
FLOYDTRI PROLOG
L      R5,NN              nn
BCTR   R5,0               -1
M      R4,NN              nn*(nn-1)
SRA    R5,1               /2
A      R5,NN              m=(nn*(nn-1))/2+nn; max_value
CVD    R5,XDEC            binary to packed decimal (PL8)
EDMK   ZN,XDEC+4          packed dec (PL4) to char (CL8)
S      R1,=A(ZN)          r1=number of spaces
L      R9,=A(L'ZN+1)      length(zn08)+1
SR     R9,R1              s=length(m)+1
SR     R8,R8              k=0
LA     R6,1               i=1
DO WHILE=(C,R6,LE,NN)       do i=1 to nn
LA     R10,PG               pgi=0
LA     R7,1                 j=1
DO WHILE=(CR,R7,LE,R6)          do j=1 to i
LA     R8,1(R8)               k=k+1
XDECO  R8,XDEC                k
LA     R11,XDEC+12            +12
SR     R11,R9                 -s
LR     R2,R9                  s
BCTR   R2,0                   -1
EX     R2,MVCX                mvc @PG+pgi,@XDEC+12-s,LEN=s
AR     R10,R9                 pgi+=s
LA     R7,1(R7)               j++
ENDDO    ,                    enddo j
XPRNT  PG,L'PG              print buffer
LA     R6,1(R6)             i++
ENDDO    ,                  enddo i
EPILOG
MVCX     MVC    0(0,R10),0(R11)    mvc PG,XDEC
NN       DC     F'14'              number of rows
PG       DC     CL80' '            buffer
XDEC     DS     CL12               temp
ZN       DC     X'4020202020202020'  mask CL8 7num
YREGS
END    FLOYDTRI```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```
Output:
```   1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

## ABAP

``` REPORT zmbr_test.

PARAMETERS: p_row TYPE i.

START-OF-SELECTION.

DATA(lv_column) = 0.
DATA(lv_number) = 0.

DO p_row TIMES.

lv_column += 1.

DO lv_column TIMES.

lv_number += 1.

WRITE: lv_number.

ENDDO.

WRITE:/ space.

ENDDO.
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```
Output:
```   1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
```

## ABC

```HOW TO RETURN width n:
SELECT:
n<10: RETURN 1
ELSE: RETURN 1 + width floor (n/10)

HOW TO DISPLAY A FLOYD TRIANGLE WITH lines LINES:
PUT lines * (lines+1)/2 IN maxno
PUT 1 IN n
FOR line IN {1..lines}:
FOR col IN {1..line}:
WRITE n >> (1 + width (maxno - lines + col))
PUT n+1 IN n
WRITE /

DISPLAY A FLOYD TRIANGLE WITH 5 LINES
WRITE /
DISPLAY A FLOYD TRIANGLE WITH 14 LINES
WRITE /```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Action!

```PROC Triangle(BYTE level)
INT v,i
BYTE x,y
BYTE ARRAY widths(20)
CHAR ARRAY tmp(5)

v=1
FOR y=1 TO level-1
DO
v==+y
OD
FOR x=0 TO level-1
DO
StrI(v+x,tmp)
widths(x)=tmp(0)
OD

v=1
FOR y=1 TO level
DO
FOR x=0 TO y-1
DO
StrI(v,tmp)
FOR i=tmp(0) TO widths(x)-1
DO
Put(32)
OD
Print(tmp)
IF x<y-1 THEN
Put(32)
ELSE
PutE()
FI
v==+1
OD
OD
RETURN

PROC Main()
BYTE LMARGIN=\$52,oldLMARGIN

oldLMARGIN=LMARGIN
LMARGIN=0 ;remove left margin on the screen

Put(125) PutE() ;clear the screen
Triangle(5)
PutE()
Triangle(13)

LMARGIN=oldLMARGIN ;restore left margin on the screen
RETURN```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
```

```with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Command_Line;

procedure Floyd_Triangle is
rows : constant Natural := Natural'Value(Ada.Command_Line.Argument(1));
begin
for r in 1..rows loop
for i in 1..r loop
end loop;
end loop;
end Floyd_Triangle;
```
Output:
```> ./floyd_triangle_triangle 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

> ./floyd_triangle 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## ALGOL 68

Works with: ALGOL 68G version Any - tested with release 2.8.win32
```# procedure to print a Floyd's Triangle with n lines                      #
PROC floyds triangle = ( INT n )VOID:
BEGIN

# calculate the number of the highest number that will be printed     #
# ( the sum of the integers 1, 2, ... n )                             #
INT max number = ( n * ( n + 1 ) ) OVER 2;

# determine the widths required to print the numbers of the final row #
[ n ]INT widths;
INT number := max number + 1;
FOR col FROM n BY -1 TO 1 DO
widths[ col ] := - ( UPB whole( number -:= 1, 0 ) + 1 )
OD;

# print the triangle                                                  #
INT element := 0;
FOR row TO n DO
FOR col TO row DO
print( ( whole( element +:= 1, widths[ col ] ) ) )
OD;
print( ( newline ) )
OD

END; # floyds triangle #

main: (

floyds triangle(  5 );
print( ( newline ) );
floyds triangle( 14 )

)```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## ALGOL W

Translation of: ALGOL_68
```begin
% prints a Floyd's Triangle with n lines                                  %
procedure floydsTriangle ( integer value n ) ;
begin
% the triangle should be left aligned with the individual numbers     %
% right-aligned with only one space before the number in the final    %
% row                                                                 %
% calculate the highest number that will be printed                   %
% ( the sum of the integeregers 1, 2, ... n )                         %
integer array widths( 1 :: n );
integer maxNumber, number;
maxNumber := ( n * ( n + 1 ) ) div 2;
% determine the widths required to print the numbers of the final row %
number := maxNumber;
for col := n step -1 until 1 do begin
integer v, w;
w      := 0;
v      := number;
number := number - 1;
while v > 0 do begin
w  := w + 1;
v  := v div 10
end while_v_gt_0 ;
widths( col ) := w
end for_col;
% print the triangle                                                  %
number := 0;
for row := 1 until n do begin
for col := 1 until row do begin
number := number + 1;
writeon( i_w := widths( col ), s_w := 0, " ", number )
end for_col ;
write()
end for_row
end; % floyds triangle %

floydsTriangle(  5 );
write();
floydsTriangle( 14 )

end.```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## APL

Works with: Dyalog APL
```floyd←{
max←⍵×(⍵+1)÷2
tri←↑(⍳max)⊂⍨(0,⍳max-1)∊+\0,⍳⍵
wdt←⌈⍀⊖≢∘⍕¨tri
↑,/wdt{' ',(-⍺××⍵)↑⍕⍵}¨tri
}
```
Output:
```      floyd 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
floyd 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## AppleScript

### Functional

Translation of: JavaScript

(mapAccumL versions)

```-- FLOYDs TRIANGLE -----------------------------------------------------------

-- floyd :: Int -> [[Int]]
on floyd(n)
script floydRow
on |λ|(start, row)
{start + row + 1, enumFromTo(start, start + row)}
end |λ|
end script

snd(mapAccumL(floydRow, 1, enumFromTo(0, n - 1)))
end floyd

-- showFloyd :: [[Int]] -> String
on showFloyd(xss)
set ws to map(compose({my succ, my |length|, my show}), |last|(xss))

script aligned
on |λ|(xs)
on |λ|(w, x)
justifyRight(w, space, show(x))
end |λ|
end script

end |λ|
end script

unlines(map(aligned, xss))
end showFloyd

-- TEST ----------------------------------------------------------------------
on run
script test
on |λ|(n)
showFloyd(floyd(n)) & linefeed
end |λ|
end script

unlines(map(test, {5, 14}))
end run

-- GENERIC FUNCTIONS ---------------------------------------------------------

-- compose :: [(a -> a)] -> (a -> a)
on compose(fs)
script
on |λ|(x)
script
on |λ|(f, a)
mReturn(f)'s |λ|(a)
end |λ|
end script

foldr(result, x, fs)
end |λ|
end script
end compose

-- concat :: [[a]] -> [a] | [String] -> String
on concat(xs)
if length of xs > 0 and class of (item 1 of xs) is string then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to length of xs
set acc to acc & item i of xs
end repeat
acc
end concat

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- foldr :: (b -> a -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(item i of xs, v, i, xs)
end repeat
return v
end tell
end foldr

-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate

-- justifyRight :: Int -> Char -> Text -> Text
on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight

-- last :: [a] -> a
on |last|(xs)
if length of xs > 0 then
item -1 of xs
else
missing value
end if
end |last|

-- length :: [a] -> Int
on |length|(xs)
length of xs
end |length|

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- 'The mapAccumL function behaves like a combination of map and foldl;
-- it applies a function to each element of a list, passing an
-- accumulating parameter from left to right, and returning a final
-- value of this accumulator together with the new list.' (see Hoogle)

-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
on mapAccumL(f, acc, xs)
script
on |λ|(a, x)
tell mReturn(f) to set pair to |λ|(item 1 of a, x)
[item 1 of pair, (item 2 of a) & {item 2 of pair}]
end |λ|
end script

foldl(result, [acc, []], xs)
end mapAccumL

-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length

-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}

repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate

-- snd :: (a, b) -> b
on snd(xs)
if class of xs is list and length of xs > 1 then
item 2 of xs
else
missing value
end if
end snd

-- show :: a -> String
on show(e)
set c to class of e
if c = list then
script serialized
on |λ|(v)
show(v)
end |λ|
end script

"{" & intercalate(", ", map(serialized, e)) & "}"
else if c = record then
script showField
on |λ|(kv)
set {k, v} to kv
k & ":" & show(v)
end |λ|
end script

"{" & intercalate(", ", ¬
map(showField, zip(allKeys(e), allValues(e)))) & "}"
else if c = date then
("date \"" & e as text) & "\""
else if c = text then
"\"" & e & "\""
else
try
e as text
on error
("«" & c as text) & "»"
end try
end if
end show

-- succ :: Int -> Int
on succ(x)
x + 1
end succ

-- unlines :: [String] -> String
on unlines(xs)
intercalate(linefeed, xs)
end unlines

-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end zipWith
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

Or, defining only the relationship between successive terms:

```-- floyd :: [Int] -> [Int]
on floyd(xs)
set n to succ(length of xs)
if n < 2 then
{1}
else
enumFromTo(succ(n * (pred(n)) div 2), n * (succ(n)) div 2)
end if
end floyd

-- floydN :: Int -> [[Int]]
on floydN(n)
take(n, iterate(floyd, {1}))
end floydN

-- showFloyd :: [[Int]] -> String
on showFloyd(xs)
script
on |λ|(ns)
script
on |λ|(n)
justifyRight(4, space, n as string)
end |λ|
end script
concat(map(result, ns))
end |λ|
end script
unlines(map(result, xs))
end showFloyd

-- TEST -------------------------------------------------------------
on run

showFloyd(floydN(5))

end run

-- GENERIC ABSTRACTIONS ---------------------------------------

-- concat :: [[a]] -> [a]
-- concat :: [String] -> String
on concat(xs)
set lng to length of xs
if 0 < lng and string is class of (item 1 of xs) then
set acc to ""
else
set acc to {}
end if
repeat with i from 1 to lng
set acc to acc & item i of xs
end repeat
acc
end concat

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo

-- iterate :: (a -> a) -> a -> Gen [a]
on iterate(f, x)
script
property v : missing value
property g : mReturn(f)'s |λ|
on |λ|()
if missing value is v then
set v to x
else
set v to g(v)
end if
return v
end |λ|
end script
end iterate

-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller, strText)
if n > length of strText then
text -n thru -1 of ((replicate(n, cFiller) as text) & strText)
else
strText
end if
end justifyRight

-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- pred :: Int -> Int
on pred(x)
(-1) + x
end pred

-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> a -> [a]
on replicate(n, a)
set out to {}
if n < 1 then return out
set dbl to {a}

repeat while (n > 1)
if (n mod 2) > 0 then set out to out & dbl
set n to (n div 2)
set dbl to (dbl & dbl)
end repeat
return out & dbl
end replicate

-- succ :: Int -> Int
on succ(x)
1 + x
end succ

-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to xs's |λ|()
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take

-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
```
Output:
```   1
2   3
4   5   6
7   8   9  10
11  12  13  14  15```

Or as a partially populated matrix:

```--------------------- FLOYD'S TRIANGLE -------------------

-- floyd :: Int -> [[Maybe Int]]
on floyd(n)
script go
on |λ|(y, x)
if x ≤ y then
x + (y * (y - 1)) div 2
else
missing value
end if
end |λ|
end script

matrix(n, n, go)
end floyd

--------------------------- TEST -------------------------
on run
-- Floyd triangles of dimensions 5 and 14

unlines(map(compose(showMatrix, floyd), {5, 14}))

end run

------------------------- GENERIC ------------------------

-- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
on compose(f, g)
script
property mf : mReturn(f)
property mg : mReturn(g)
on |λ|(x)
mf's |λ|(mg's |λ|(x))
end |λ|
end script
end compose

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set xs to {}
repeat with i from m to n
set end of xs to i
end repeat
xs
else
{}
end if
end enumFromTo

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- justifyRight :: Int -> Char -> String -> String
on justifyRight(n, cFiller)
script
on |λ|(s)
if n > length of s then
text -n thru -1 of ((replicate(n, cFiller) as text) & s)
else
s
end if
end |λ|
end script
end justifyRight

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- matrix :: Int -> Int -> ((Int, Int) -> a) -> [[a]]
on matrix(nRows, nCols, f)
-- A matrix of a given number of columns and rows,
-- in which each value is a given function of its
-- (zero-based) column and row indices.
script go
property g : mReturn(f)'s |λ|
on |λ|(iRow)
set xs to {}
repeat with iCol from 1 to nCols
set end of xs to g(iRow, iCol)
end repeat
xs
end |λ|
end script

map(go, enumFromTo(1, nRows))
end matrix

-- max :: Ord a => a -> a -> a
on max(x, y)
if x > y then
x
else
y
end if
end max

-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- Egyptian multiplication - progressively doubling a list, appending
-- stages of doubling to an accumulator where needed for binary
-- assembly of a target length
-- replicate :: Int -> String -> String
on replicate(n, s)
-- Egyptian multiplication - progressively doubling a list,
-- appending stages of doubling to an accumulator where needed
-- for binary assembly of a target length
script p
on |λ|({n})
n ≤ 1
end |λ|
end script

script f
on |λ|({n, dbl, out})
if (n mod 2) > 0 then
set d to out & dbl
else
set d to out
end if
{n div 2, dbl & dbl, d}
end |λ|
end script

set xs to |until|(p, f, {n, s, ""})
item 2 of xs & item 3 of xs
end replicate

-- showMatrix :: [[Maybe a]] -> String
on showMatrix(rows)
-- String representation of rows
-- as a matrix.

script showRow
on |λ|(a, row)
set {maxWidth, prevRows} to a
script showCell
on |λ|(acc, cell)
set {w, xs} to acc
if missing value is cell then
{w, xs & ""}
else
set s to cell as string
{max(w, length of s), xs & s}
end if
end |λ|
end script

set {rowMax, cells} to foldl(showCell, {0, {}}, row)
{max(maxWidth, rowMax), prevRows & {cells}}
end |λ|
end script

set {w, stringRows} to foldl(showRow, {0, {}}, rows)
script go
on |λ|(row)
unwords(map(justifyRight(w, space), row))
end |λ|
end script

unlines(map(go, stringRows)) & linefeed
end showMatrix

-- str :: a -> String
on str(x)
x as string
end str

-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines

-- until :: (a -> Bool) -> (a -> a) -> a -> a
on |until|(p, f, x)
set v to x
set mp to mReturn(p)
set mf to mReturn(f)
repeat until mp's |λ|(v)
set v to mf's |λ|(v)
end repeat
v
end |until|

-- unwords :: [String] -> String
on unwords(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, space}
set s to xs as text
set my text item delimiters to dlm
return s
end unwords
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

### Straightforward

```on FloydsTriangle(n)
set triangle to {}
set i to 0
repeat with w from 1 to n
set row to {}
repeat with i from (i + 1) to (i + w)
set end of row to i
end repeat
set end of triangle to row
end repeat

return triangle
end FloydsTriangle

on matrixToText(matrix, w)
script o
property matrix : missing value
property row : missing value
end script

set o's matrix to matrix
repeat with r from 1 to (count o's matrix)
set o's row to o's matrix's item r
repeat with i from 1 to (count o's row)
set o's row's item i to text -w thru end of (padding & o's row's item i)
end repeat
set o's matrix's item r to join(o's row, "")
end repeat

return join(o's matrix, linefeed)
end matrixToText

on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join

local triangle5, text5, triangle14, text14
set triangle5 to FloydsTriangle(5)
set text5 to matrixToText(triangle5, (count (end of end of triangle5 as text)) + 1)
set triangle14 to FloydsTriangle(14)
set text14 to matrixToText(triangle14, (count (end of end of triangle14 as text)) + 1)
return linefeed & text5 & (linefeed & linefeed & text14 & linefeed)
```
Output:
```"
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
"
```

## Arturo

```width: function [rows col] .memoize [
floor 2 + log col + 1 + (rows * rows - 1) / 2 10
]

floyd: function [rows][
n: 1
row: 1
col: 0
while -> row =< rows [
prints pad ~"|n|" width rows col
inc 'col
inc 'n
if col = row [
print ""
col: 0
inc 'row
]
]
]

floyd 5
print ""
floyd 14
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## AutoHotkey

```Floyds_triangle(row){
i = 0
loop %row%
{
n := A_Index
loop, %n%
{
m := n, j := i, i++
while (m<row)
j += m , m++
res .= spaces(StrLen(j+1)-StrLen(i) +(A_Index=1?0:1)) i
}
if (A_Index < row)
res .= "`r`n"
}
return res
}
Spaces(no){
loop, % no
res.=" "
return % res
}
```

Examples:

```MsgBox % Floyds_triangle(14)
```

Outputs:

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## AWK

```#!/bin/awk -f

BEGIN {
if (rows !~ /^[0-9]+\$/ || rows < 0) {
print "invalid rows or missing from command line"
print "syntax: awk -v rows=14 -f floyds_triangle.awk"
exit 1
}

for (row=cols=1; row<=rows; row++ cols++) {
width[row] = length(row + (rows * (rows-1))/2)
for (col=1; col<=cols; col++)
printf("%*d%c", width[col], ++n, row == col ? "\n" : " ")
}
}
```

output from: awk -f floyds_triangle.awk -v rows=5

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```

output from: awk -f floyds_triangle.awk -v rows=14

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## BASIC

### Applesoft BASIC

Line `150,160` creates a vector of the length of all entries is the last row. These values are used in line `210,220` to put the cursor at the correct horizontal position.

``` 100 :
110  REM  FLOYD'S TRIANGLE
120 :
130  DEF  FN Q(A) =  INT ( LOG (A) /  LOG (10)) + 1
140 N = 14
150  DIM P(N): P(0) =  - 1: FOR J = 1 TO N: I = (N * N - N) / 2 + J
160 P(J) = P(J - 1) + FN Q(I) + 1: NEXT J
200  FOR R = 1 TO N: FOR C = 1 TO R
210 NR = NR + 1:COL = P(C) - ( FN Q(NR) - 1)
220  HTAB COL: PRINT NR;: NEXT C
230  PRINT : NEXT R
```
Output:
```]RUN
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15```
```]RUN
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

### BASIC256

Works with: BASIC256 version 2.0.0.11
```function trianglevalue(col, row)
return (row-1)*row\2 + col
end function

subroutine printtriangle(numrows)
for row = 1 to numrows
for col = 1 to row-1
colwidth = length(""+trianglevalue(col, numrows))
print right(" "*colwidth+trianglevalue(col, row), colwidth);" ";
next col
colwidth = length(""+trianglevalue(col, numrows))
print right(" "*colwidth+trianglevalue(col, row), colwidth)
next row
end subroutine

call printtriangle(5)
print
call printtriangle(14)```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

### BBC BASIC

```      n = 14
num = 1
last = (n^2 - n + 2) DIV 2
FOR row = 1 TO n
col = last
FOR num = num TO num + row - 1
@% = LEN(STR\$(col)) + 1 : REM set column width
PRINT num ;
col += 1
NEXT
PRINT
NEXT row
```

Output for n = 5:

```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```

Output for n = 14:

```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

### Chipmunk Basic

Works with: Chipmunk Basic version 3.6.4
Works with: Applesoft BASIC
Works with: BASICA
Works with: GW-BASIC
Works with: PC-BASIC
Works with: QBasic
Works with: QuickBasic
Works with: Just BASIC
Works with: Liberty BASIC
Works with: Run BASIC
```100 CLS : REM  100 HOME for Applesoft BASIC
110 INPUT "Number of rows: "; ROWS
120 DIM COLSIZE(ROWS)
130 FOR COL = 1 TO ROWS
140   COLSIZE(COL) = LEN(STR\$(COL + ROWS * (ROWS - 1) / 2))
150 NEXT
160 THISNUM = 1
170 FOR R = 1 TO ROWS
180   FOR COL = 1 TO R
190     PRINT RIGHT\$("  " + STR\$(THISNUM), COLSIZE(COL)); " ";
200     THISNUM = THISNUM + 1
210   NEXT
220   PRINT
230 NEXT
240 END
```

### Commodore BASIC

```100 print chr\$(14);chr\$(147);"Floyd's triangle"
110 print "How many rows? ";
120 open 1,0:input#1,ro\$:close 1:print
130 ro=val(ro\$):if ro<1 then 110
140 li=ro*(ro+1)/2
150 dim w(ro-1)
160 n=li-ro+1
170 for i=0 to ro-1:w(i)=len(str\$(n)):n=n+1:next i
180 n=1
190 for i=1 to ro
200 : for j=0 to i-1
210 :  n\$=mid\$(str\$(n),2)
220 :  if len(n\$)<w(j) then for k=1 to w(j)-len(n\$):print" ";:next k
230 :  print n\$;
240 :  n=n+1
250 : next j
260 : print
270 next i
280 end
```
Output:
```Floyd's triangle
How many rows? 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

How many rows? 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

### GW-BASIC

The Chipmunk Basic solution works without any changes.

### IS-BASIC

 This example is incorrect. Please fix the code and remove this message.Details: last line should only have one space between values
```100 PROGRAM "FloydT.bas"
110 LET N=14:LET J=1
120 TEXT 80
130 FOR I=1 TO N
140   FOR J=J TO J+I-1
150     PRINT USING " ###":J;
160   NEXT
170   PRINT
180 NEXT```

### MasmBasic

```include \masm32\MasmBasic\MasmBasic.inc
SetGlobals rows, columns, ct, maxrows=4
Init
.Repeat
For_ rows=0 To maxrows
For_ columns=0 To rows
inc ct
Print Str\$("%__i", ct)
.if columns>6
Print " "
.endif
Next
Print
Next
Print
Clr ct
.Until maxrows>13
Inkey
EndOfCode```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

### MSX Basic

The Chipmunk Basic solution works without any changes.

### QBasic

```SUB FloydTriangle (fila)
DIM numColum(fila)
FOR colum = 1 TO fila
numColum(colum) = LEN(STR\$(colum + fila * (fila - 1) / 2))
NEXT colum

PRINT "output for "; STR\$(fila): PRINT
thisNum = 1
FOR r = 1 TO fila
FOR colum = 1 TO r
PRINT RIGHT\$("  " + STR\$(thisNum), numColum(colum)); " ";
thisNum = thisNum + 1
NEXT colum
PRINT
NEXT
END SUB

FloydTriangle (5)
PRINT
FloydTriangle (14)
```

### True BASIC

Translation of: QBasic
```SUB floydtriangle (fila)
DIM numcolum(0)
MAT REDIM numcolum(fila)
FOR colum = 1 TO fila
LET numcolum(colum) = LEN(STR\$(colum+fila*(fila-1)/2))
NEXT colum
PRINT "output for "; STR\$(fila)
PRINT
LET thisnum = 1
FOR r = 1 TO fila
FOR colum = 1 TO r
PRINT ("  " & STR\$(thisnum))[LEN("  " & STR\$(thisnum))-numcolum(colum)+1:maxnum]; " ";
LET thisnum = thisnum+1
NEXT colum
PRINT
NEXT r
END SUB

CALL FLOYDTRIANGLE (5)
PRINT
CALL FLOYDTRIANGLE (14)
END
```

### XBasic

Works with: Windows XBasic
```PROGRAM	"Floyd's triangle"
VERSION	"0.0001"

DECLARE FUNCTION  Entry ()
DECLARE FUNCTION  FloydTriangle (n)

FUNCTION  Entry ()
FloydTriangle (5)
PRINT
FloydTriangle (14)
END FUNCTION

FUNCTION FloydTriangle (fila)
DIM numColum[fila]
FOR colum = 1 TO fila
t\$ = STR\$(colum + fila * (fila - 1) / 2)
numColum[colum] = LEN(t\$)
NEXT colum

PRINT "output for "; STR\$(fila)
PRINT
thisNum = 1
FOR r = 1 TO fila
FOR colum = 1 TO r
PRINT RIGHT\$("  " + STR\$(thisNum), numColum[colum]); " ";
INC thisNum
NEXT colum
PRINT
NEXT r
END FUNCTION
END PROGRAM
```

### Yabasic

```sub FloydTriangle (fila)
dim numColum(fila)
for colum = 1 to fila
numColum(colum) = len(str\$(colum + fila * (fila - 1) / 2))
next colum

print "output for ", str\$(fila), "\n"
thisNum = 1
for r = 1 to fila
for colum = 1 to r
print right\$("  " + str\$(thisNum), numColum(colum)), " ";
thisNum = thisNum + 1
next colum
print
next
end sub

FloydTriangle (5)
print
FloydTriangle (14)```

## Batch File

Translation of: QBasic
```:: Floyd's triangle Task from Rosetta Code
:: Batch File Implementation

@echo off
rem main thing
setlocal enabledelayedexpansion
call :floydtriangle 5
echo(
call :floydtriangle 14
exit /b 0

:floydtriangle
set "fila=%1"
for /l %%c in (1,1,%fila%) do (
set /a "lastRowNum=%%c+fila*(fila-1)/2"
rem count number of digits of whole number trick
rem source: https://stackoverflow.com/a/45472269
set /a "Log=1!lastRowNum:~1!-!lastRowNum:~1!-0"
set /a "numColum[%%c]=!Log:0=+1!"
)
echo(Output for %fila%
set "thisNum=1"
for /l %%r in (1,1,%fila%) do (
set "printLine="
for /l %%c in (1,1,%%r) do (
rem count number of digits of whole number trick
set /a "Log=1!thisNum:~1!-!thisNum:~1!-0"
set /a "thisNumColum=!Log:0=+1!"
rem handle spacing
set "space= "
set /a "extra=!numColum[%%c]!-!thisNumColum!"
for /l %%s in (1,1,!extra!) do set "space=!space! "
rem append current number to printLine
set "printLine=!printLine!!space!!thisNum!"
set /a "thisNum=!thisNum!+1"
)
echo(!printLine!
)
goto :EOF```
Output:
```Output for 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

Output for 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## BCPL

```get "libhdr"

let width(n) = n<10 -> 1, 1 + width(n/10)

let floyd(rows) be
\$(  let maxno = rows * (rows+1)/2
let num = 1
for r = 1 to rows
\$(  for c = 1 to r
\$(  writed(num, 1 + width(maxno-rows+c))
num := num + 1
\$)
wrch('*N')
\$)
\$)

let start() be
\$(  floyd(5)
wrch('*N')
floyd(14)
\$)```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Befunge

```0" :seniL">:#,_&>:!#@_55+,:00p::1+*2/1v
vv+1:\-1p01g5-\g00<v`*9"o"\+`"c"\`9:::_
\$>>\:::9`\"c"`+\9v:>>+00g1-:00p5p1-00g^
<v\*84-\g01+`*"o"<^<<p00:+1\+1/2*+1:::\
^>:#\1#,-#:\_\$\$.\:#^_\$\$>>1+\1-55+,:!#@_
```
Output:
```Lines: 5

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15```
```Lines: 14

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Bracmat

```  ( ( floyd
=   lowerLeftCorner lastInColumn lastInRow row i W w
.   put\$(str\$("Floyd " !arg ":\n"))
&   !arg*(!arg+-1)*1/2+1
: ?lowerLeftCorner
: ?lastInColumn
& 1:?lastInRow:?row:?i
&   whl
' ( !row:~>!arg
& @(!lastInColumn:? [?W)
& @(!i:? [?w)
& whl'(!w+1:~>!W:?w&put\$" ")
& put\$!i
& (   !i:<!lastInRow
& put\$" "
& 1+!lastInColumn:?lastInColumn
|   put\$\n
& (1+!row:?row)+!lastInRow:?lastInRow
& !lowerLeftCorner:?lastInColumn
)
& 1+!i:?i
)
)
& floyd\$5
& floyd\$14
);```

Output:

```Floyd 5:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
Floyd 14:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## C

```#include <stdio.h>

void t(int n)
{
int i, j, c, len;

i = n * (n - 1) / 2;
for (len = c = 1; c < i; c *= 10, len++);
c -= i; // c is the col where width changes

#define SPEED_MATTERS 0
#if SPEED_MATTERS	// in case we really, really wanted to print huge triangles often
char tmp[32], s[4096], *p;

sprintf(tmp, "%*d", len, 0);

inline void inc_numstr(void) {
int k = len;

redo:	if (!k--) return;

if (tmp[k] == '9') {
tmp[k] = '0';
goto redo;
}

if (++tmp[k] == '!')
tmp[k] = '1';
}

for (p = s, i = 1; i <= n; i++) {
for (j = 1; j <= i; j++) {
inc_numstr();
__builtin_memcpy(p, tmp + 1 - (j >= c), len - (j < c));
p += len - (j < c);

*(p++) = (i - j)? ' ' : '\n';

if (p - s + len >= 4096) {
fwrite(s, 1, p - s, stdout);
p = s;
}
}
}

fwrite(s, 1, p - s, stdout);
#else // NO_IT_DOESN'T
int num;
for (num = i = 1; i <= n; i++)
for (j = 1; j <= i; j++)
printf("%*d%c",	len - (j < c), num++, i - j ? ' ':'\n');
#endif
}

int main(void)
{
t(5), t(14);

// maybe not
// t(10000);
return 0;
}
```

Output identical to D's.

## C#

Translation of: Perl
```using System;
using System.Text;

public class FloydsTriangle
{
internal static void Main(string[] args)
{
int count;
if (args.Length >= 1 && int.TryParse(args[0], out count) && count > 0)
{
Console.WriteLine(MakeTriangle(count));
}
else
{
Console.WriteLine(MakeTriangle(5));
Console.WriteLine();
Console.WriteLine(MakeTriangle(14));
}
}

public static string MakeTriangle(int rows)
{
int maxValue = (rows * (rows + 1)) / 2;
int digit = 0;
StringBuilder output = new StringBuilder();

for (int row = 1; row <= rows; row++)
{
for (int column = 0; column < row; column++)
{
int colMaxDigit = (maxValue - rows) + column + 1;
if (column > 0)
{
output.Append(' ');
}

digit++;
}

output.AppendLine();
}

return output.ToString();
}
}
```

## C++

```#include <windows.h>
#include <sstream>
#include <iostream>

//--------------------------------------------------------------------------------------------------
using namespace std;

//--------------------------------------------------------------------------------------------------
class floyds_tri
{
public:
floyds_tri()  { lastLineLen = 0; }
~floyds_tri() { killArray(); }

void create( int rows )
{
_rows = rows;
calculateLastLineLen();
display();
}

private:
void killArray()
{
if( lastLineLen )
delete [] lastLineLen;
}

void calculateLastLineLen()
{
killArray();
lastLineLen = new BYTE[_rows];

int s = 1 + ( _rows * ( _rows - 1 ) ) / 2;

for( int x = s, ix = 0; x < s + _rows; x++, ix++ )
{
ostringstream cvr;
cvr << x;
lastLineLen[ix] = static_cast<BYTE>( cvr.str().size() );
}
}

void display()
{
cout << endl << "Floyd\'s Triangle - " << _rows << " rows" << endl << "===============================================" << endl;
int number = 1;
for( int r = 0; r < _rows; r++ )
{
for( int c = 0; c <= r; c++ )
{
ostringstream cvr;
cvr << number++;
string str = cvr.str();
while( str.length() < lastLineLen[c] )
str = " " + str;
cout << str << " ";
}
cout << endl;
}
}

int _rows;
BYTE* lastLineLen;
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
floyds_tri t;
int s;
while( true )
{
cout << "Enter the size of the triangle ( 0 to QUIT ): "; cin >> s;
if( !s ) return 0;
if( s > 0 ) t.create( s );

cout << endl << endl;
system( "pause" );
}

return 0;
}
//--------------------------------------------------------------------------------------------------
```
Output:
```Floyd's Triangle - 5 rows
===============================================
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

Floyd's Triangle - 14 rows
===============================================
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Clojure

I didn't translete this, it's from my own creation.

```(defn TriangleList [n]
(let [l (map inc (range))]
(loop [l l x 1 nl []]
(if (= n (count nl))
nl
(recur (drop x l) (inc x) (conj nl (take x l)))))))

(defn TrianglePrint [n]
(let [t (TriangleList n)
m (count (str (last (last t))))
f (map #(map str %) t)
l (map #(map (fn [x] (if (> m (count x))
(str (apply str (take (- m (count x))
(repeat " "))) x)
x)) %) f)
e (map #(map (fn [x] (str " " x)) %) l)]
(map #(println (apply str %)) e)))
```

By Average-user.

Output:
```(TrianglePrint 5)
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

(TrianglePrint 14)
1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

## CLU

```floyd = cluster is triangle
rep = null

width = proc (n: int) returns (int)
w: int := 1
while n >= 10 do
w := w + 1
n := n / 10
end
return (w)
end width

triangle = proc (rows: int) returns (string)
ss: stream := stream\$create_output()
maxno: int := rows * (rows+1)/2
num: int := 1
for row: int in int\$from_to(1, rows) do
for col: int in int\$from_to(1, row) do
stream\$putright(ss, int\$unparse(num), 1 + width(maxno-rows+col))
num := num + 1
end
stream\$putl(ss, "")
end
return (stream\$get_contents(ss))
end triangle
end floyd

start_up = proc ()
po: stream := stream\$primary_output()
stream\$putl(po, floyd\$triangle(5))
stream\$putl(po, floyd\$triangle(14))
end start_up```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## COBOL

```        IDENTIFICATION DIVISION.
PROGRAM-ID. FLOYD-TRIANGLE.

DATA DIVISION.
WORKING-STORAGE SECTION.
01 VARIABLES        COMP.
02 NUM-LINES     PIC 99.
02 CUR-LINE      PIC 99.
02 CUR-COL       PIC 99.
02 CUR-NUM       PIC 999.
02 ZERO-SKIP     PIC 9.
02 LINE-PTR      PIC 99.
02 MAX-NUM       PIC 999.

01 OUTPUT-FORMAT.
02 OUT-LINE      PIC X(72).
02 ONE-DIGIT     PIC B9.
02 TWO-DIGITS    PIC BZ9.
02 THREE-DIGITS  PIC BZZ9.
02 MAX-COL-NUM   PIC 999.

PROCEDURE DIVISION.
BEGIN.
MOVE 5 TO NUM-LINES. PERFORM FLOYD.
DISPLAY ' '.
MOVE 14 TO NUM-LINES. PERFORM FLOYD.
STOP RUN.

FLOYD.
MOVE 1 TO CUR-NUM.
COMPUTE MAX-NUM = NUM-LINES * (NUM-LINES + 1) / 2.
PERFORM FLOYD-LINE
VARYING CUR-LINE FROM 1 BY 1
UNTIL CUR-LINE IS GREATER THAN NUM-LINES.

FLOYD-LINE.
MOVE ' ' TO OUT-LINE.
MOVE 1 TO LINE-PTR.
PERFORM FLOYD-NUM
VARYING CUR-COL FROM 1 BY 1
UNTIL CUR-COL IS GREATER THAN CUR-LINE.
DISPLAY OUT-LINE.

FLOYD-NUM.
COMPUTE MAX-COL-NUM = MAX-NUM - NUM-LINES + CUR-COL.
MOVE 0 TO ZERO-SKIP.
INSPECT MAX-COL-NUM TALLYING ZERO-SKIP FOR LEADING '0'.
IF ZERO-SKIP IS EQUAL TO ZERO
PERFORM FLOYD-THREE-DIGITS
ELSE IF ZERO-SKIP IS EQUAL TO 1
PERFORM FLOYD-TWO-DIGITS
ELSE IF ZERO-SKIP IS EQUAL TO 2
PERFORM FLOYD-ONE-DIGIT.

FLOYD-ONE-DIGIT.
MOVE CUR-NUM TO ONE-DIGIT.
STRING ONE-DIGIT DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.

FLOYD-TWO-DIGITS.
MOVE CUR-NUM TO TWO-DIGITS.
STRING TWO-DIGITS DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.

FLOYD-THREE-DIGITS.
MOVE CUR-NUM TO THREE-DIGITS.
STRING THREE-DIGITS DELIMITED BY SIZE INTO OUT-LINE
WITH POINTER LINE-PTR.
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## CoffeeScript

Translation of: Kotlin
```triangle = (array) -> for n in array
console.log "#{n} rows:"
printMe = 1
printed = 0
row = 1
to_print = ""
while row <= n
cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0))
p = ("" + printMe).length
while p++ <= cols
to_print += ' '
to_print += printMe + ' '
if ++printed == row
console.log to_print
to_print = ""
row++
printed = 0
printMe++

triangle [5, 14]
```

Output as Kotlin.

## Common Lisp

### Version 1

```;;;using flet to define local functions and storing precalculated column widths in array
;;;verbose, but more readable and efficient than version 2

(defun floydtriangle (rows)
(let (column-widths)
(setf column-widths (make-array rows :initial-element nil))
(flet (
(lazycat (n)
(/ (+ (expt n 2) n 2) 2))
(width (v)
(+ 1 (floor (log v 10)))))
(dotimes (i rows)
(setf (aref column-widths i)(width (+ i (lazycat (- rows 1))))))
(dotimes (row rows)
(dotimes (col (+ 1 row))
(format t "~vd " (aref column-widths col)(+ col (lazycat row))))
(format t "~%")))))
```

### Version 2 - any base

```;;; more concise than version 1 but less efficient for a large triangle
;;;optional "base" parameter will allow use of any base from 2 to 36

(defun floydtriangle (rows &optional (base 10))
(dotimes (row rows)
(dotimes (column (+ 1 row))
(format t "~v,vr " base (length (format nil "~vr" base (+ column (/ (+ (expt (- rows 1) 2) (- rows 1) 2) 2)))) (+ column (/ (+ (expt row 2) row 2) 2))))
(format t "~%")))
```
Output:
```(floydtriangle 5)
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

(floydtriangle 14)
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105

(floydtriangle 5 2)
1
10   11
100  101  110
111 1000 1001 1010
1011 1100 1101 1110 1111

(floydtriangle 14 36)
1
2  3
4  5  6
7  8  9  A
B  C  D  E  F
G  H  I  J  K  L
M  N  O  P  Q  R  S
T  U  V  W  X  Y  Z 10
11 12 13 14 15 16 17 18 19
1A 1B 1C 1D 1E 1F 1G 1H 1I 1J
1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T 1U
1V 1W 1X 1Y 1Z 20 21 22 23 24 25 26
27 28 29 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J
2K 2L 2M 2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X
```

## Cowgol

```include "cowgol.coh";

sub width(n: uint16): (w: uint8) is
w := 1;
while n >= 10 loop
n := n / 10;
w := w + 1;
end loop;
end sub;

sub print_fixed(n: uint16, w: uint8) is
w := w - width(n);
while w > 0 loop
print_char(' ');
w := w - 1;
end loop;
print_i16(n);
end sub;

sub floyd(rows: uint16) is
var maxno := rows * (rows+1)/2;
var num: uint16 := 1;
var row: uint16 := 1;
while row <= rows loop
var col: uint16 := 1;
while col <= row loop
print_fixed(num, 1 + width(maxno - rows + col));
num := num + 1;
col := col + 1;
end loop;
print_nl();
row := row + 1;
end loop;
end sub;

floyd(5);
print_nl();
floyd(14);```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## D

```import std.stdio, std.conv;

void floydTriangle(in uint n) {
immutable lowerLeftCorner = n * (n - 1) / 2 + 1;
foreach (r; 0 .. n)
foreach (c; 0 .. r + 1)
writef("%*d%c",
text(lowerLeftCorner + c).length,
r * (r + 1) / 2 + c + 1,
c == r ? '\n' : ' ');
}

void main() {
floydTriangle(5);
floydTriangle(14);
}
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Delphi

Works with: Delphi version 6.0

```procedure FloydsTriangle(Memo: TMemo; Rows: integer);
var I,R,C: integer;
var S: string;
begin
I:=1;
S:='';
for R:=1 to Rows do
begin
for C:=1 to R do
begin
S:=S+Format('%4d',[I]);
Inc(I);
end;
S:=S+#\$0D#\$0A;
end;
end;

procedure ShowFloydsTriangles(Memo: TMemo);
begin
FloydsTriangle(Memo,5);
FloydsTriangle(Memo,14);
end;
```
Output:
```   1
2   3
4   5   6
7   8   9  10
11  12  13  14  15

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

## Draco

```proc width(word n) word:
word w;
w := 0;
while n>0 do
w := w + 1;
n := n / 10
od;
w
corp

proc floyd(word rows) void:
word n, row, col, maxno;
maxno := rows * (rows+1)/2;
n := 1;
for row from 1 upto rows do
for col from 1 upto row do
write(n : 1+width(maxno - rows + col));
n := n+1
od;
writeln()
od
corp

proc main() void:
floyd(5);
writeln();
floyd(14)
corp```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## EasyLang

Translation of: Java
```func ceil h .
f = floor h
if h <> f
f += 1
.
return f
.
proc triangle n . .
print n & " rows:"
row = 1
while row <= n
printme += 1
cols = ceil log10 (n * (n - 1) / 2 + nprinted + 2)
numfmt 0 cols
write printme & " "
nprinted += 1
if nprinted = row
print ""
row += 1
nprinted = 0
.
.
print ""
.
triangle 5
triangle 14```
Output:
```5 rows:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

14 rows:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Elixir

```defmodule Floyd do
def triangle(n) do
max = trunc(n * (n + 1) / 2)
widths = for m <- (max - n + 1)..max, do: (m |> Integer.to_string |> String.length) + 1
format = Enum.map(widths, fn wide -> "~#{wide}w" end) |> List.to_tuple
line(n, 0, 1, format)
end

def line(n, n, _, _), do: :ok
def line(n, i, count, format) do
Enum.each(0..i, fn j -> :io.fwrite(elem(format,j), [count+j]) end)
IO.puts ""
line(n, i+1, count+i+1, format)
end
end

Floyd.triangle(5)
Floyd.triangle(14)
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Erlang

```-module( floyds_triangle ).

-export( [integers/1, print/1, strings/1, task/0] ).

integers( N ) ->
lists:reverse( integers_reversed(N) ).

print( N ) ->
[io:fwrite("~s~n", [lists:flatten(X)]) || X <- strings(N)].

strings( N ) ->
Strings_reversed = [strings_from_integers(X) || X <- integers_reversed(N)],
[formats(X, Y) || {X, Y} <- lists:zip(Paddings, lists:reverse(Strings_reversed))].

print( 5	),
print( 14 ).

formats( Paddings, Strings ) -> [lists:flatten(io_lib:format(" ~*s", [X, Y])) || {X, Y} <- lists:zip(Paddings, Strings)].

integers_reversed( N ) ->
{_End, Integers_reversed} = lists:foldl( fun integers_reversed/2, {1, []}, lists:seq(0, N - 1) ),
Integers_reversed.

integers_reversed( N, {Start, Acc} ) ->
End = Start + N,
{End + 1, [lists:seq(Start, End) | Acc]}.

lengths( Strings ) -> [string:len(X) || X <- Strings].

paddings( [Last_line | T] ) ->

[_H | T]	= lists:reverse( List ),
lists:reverse( T ).

strings_from_integers( Integers ) -> [erlang:integer_to_list(X) || X <- Integers].
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## ERRE

```PROGRAM FLOYD

!
! for rosettacode.org
!

BEGIN
N=14
NUM=1
LAST=(N^2-N+2) DIV 2
FOR ROW=1 TO N DO
FOR J=1 TO ROW DO
US\$=STRING\$(LEN(STR\$(LAST-1+J))-1,"#")
WRITE(US\$;NUM;)
PRINT(" ";)
NUM+=1
END FOR
PRINT
END FOR
END PROGRAM```

Example for n=14

Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Excel

### LAMBDA

We can define this declaratively in Excel by binding the name floydTriangle to the following lambda expression in the Name Manager of the Excel WorkBook:

```floydTriangle
=LAMBDA(n,
IF(0 < n,
LET(
ixs, SEQUENCE(
n, n,
0, 1
),
x, MOD(ixs, n),
y, QUOTIENT(ixs, n),

IF(x > y,
"",
x + 1 + QUOTIENT(
y * (1 + y),
2
)
)
),
""
)
)
```
Output:

The formula in cell B2, for example, defines an array which populates the whole range B2:F6

 =floydTriangle(A2) fx A B C D E F G H I J K L M N O 1 Row count 2 5 1 3 2 3 4 4 5 6 5 7 8 9 10 6 11 12 13 14 15 7 14 1 8 2 3 9 4 5 6 10 7 8 9 10 11 11 12 13 14 15 12 16 17 18 19 20 21 13 22 23 24 25 26 27 28 14 29 30 31 32 33 34 35 36 15 37 38 39 40 41 42 43 44 45 16 46 47 48 49 50 51 52 53 54 55 17 56 57 58 59 60 61 62 63 64 65 66 18 67 68 69 70 71 72 73 74 75 76 77 78 19 79 80 81 82 83 84 85 86 87 88 89 90 91 20 92 93 94 95 96 97 98 99 100 101 102 103 104 105

## F#

```open System

[<EntryPoint>]
let main argv =
// columns and rows are 0-based, so the input has to be decremented:
let maxRow =
match UInt32.TryParse(argv.[0]) with
| (true, v) when v > 0u -> int (v - 1u)
| (_, _) -> failwith "not a positive integer"

let len (n: int) = int (Math.Floor(Math.Log10(float n)))
let col0 row = row * (row + 1) / 2 + 1
let col0maxRow = col0 maxRow
for row in [0 .. maxRow] do
for col in [0 .. row] do
let value = (col0 row) + col
let pad = String(' ', (len (col0maxRow + col) - len (value) + 1))
printfn ""
0
```

Output for 5 and 14 (via command line argument)

```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15```
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Factor

```USING: io kernel math math.functions math.ranges prettyprint
sequences ;
IN: rosetta-code.floyds-triangle

: floyd. ( n -- )
[ dup 1 - * 2 / 1 + dup 1 ] [ [1,b] ] bi
[
[
2dup [ log10 1 + >integer ] bi@ -
[ " " write ] times dup pprint bl [ 1 + ] bi@
] times nl [ drop dup ] dip
] each nl 3drop ;

5 14 [ floyd. ] bi@
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Forth

```: lastn ( rows -- n ) dup 1- * 2/ ;
: width ( n -- n )  s>f flog ftrunc f>s 2 + ;

: triangle ( rows -- )
dup lastn 0 rot ( last 0 rows )
0 do
over cr
i 1+ 0 do
1+ swap 1+ swap
2dup width u.r
loop
drop
loop
2drop ;
```

## Fortran

Please find compilation instructions on GNU/linux system at the beginning of the source. There, also, are the example output triangles produced by running the program. The environment variable setting and command line argument are vestigial. Ignore them. The code demonstrates writing to an in memory buffer, an old feature of FORTRAN.

```!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Tue May 21 22:55:08
!
!a=./f && make \$a && OMP_NUM_THREADS=2 \$a 1223334444
!gfortran -std=f2008 -Wall -ffree-form -fall-intrinsics f.f08 -o f
!  1
!  2  3
!  4  5  6
!  7  8  9 10
! 11 12 13 14 15
!
!
!  1
!  2  3
!  4  5  6
!  7  8  9 10
! 11 12 13 14 15
! 16 17 18 19 20 21
! 22 23 24 25 26 27 28
! 29 30 31 32 33 34 35 36
! 37 38 39 40 41 42 43 44  45
! 46 47 48 49 50 51 52 53  54  55
! 56 57 58 59 60 61 62 63  64  65  66
! 67 68 69 70 71 72 73 74  75  76  77  78
! 79 80 81 82 83 84 85 86  87  88  89  90  91
! 92 93 94 95 96 97 98 99 100 101 102 103 104 105
!
!
!
!Compilation finished at Tue May 21 22:55:08

program p
integer, dimension(2) :: examples = [5, 14]
integer :: i
do i=1, size(examples)
call floyd(examples(i))
write(6, '(/)')
end do

contains

subroutine floyd(rows)
integer, intent(in) :: rows
integer :: n, i, j, k
integer, dimension(60) :: L
character(len=504) :: fmt
n = (rows*(rows+1))/2 ! Gauss's formula
do i=1,rows ! compute format of final row
L(i) = 2+int(log10(real(n-rows+i)))
end do
k = 0
do i=1,rows
do j=1,i
k = k+1
write(fmt,'(a2,i1,a1)')'(i',L(j),')'
enddo
write(6,*) ''
end do
end subroutine floyd

end program p
```

## FreeBASIC

```' version 19-09-2015
' compile with: fbc -s console

Sub pascal_triangle(n As UInteger)

Dim As UInteger a = 1, b, i, j, switch = n + 1
Dim As String frmt, frmt_1, frmt_2

' last number of the last line
i = (n * (n + 1)) \ 2
frmt_2 = String(Len(Str(i)) + 1, "#")
' first number of the last line
i = ((n - 1) * n) \ 2 + 1
frmt_1 = String(Len(Str(i)) + 1, "#")

' we have 2 different formats strings
' find the point where we have to make the switch
If frmt_1 <> frmt_2 Then
j = i + 1
While Len(Str(i)) = Len(Str(J))
j =  j + 1
Wend
switch = j - i
End If

Print "output for "; Str(n) : Print
For i = 1 To n
frmt = frmt_1
b = (i * (i + 1)) \ 2
For j = a To b
' if we have the switching point change format string
If j - a = switch Then frmt = frmt_2
Print Using frmt; j;
Next j
Print
a = b + 1
Next i
Print

End Sub

' ------=< MAIN >=------

pascal_triangle(5)

pascal_triangle(14)

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End```
Output:
```output for 5             output for 14

1                        1
2  3                     2  3
4  5  6                  4  5  6
7  8  9 10               7  8  9 10
11 12 13 14 15           11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## FutureBasic

```void local fn FloydsTriangle( rows as int )
int col, row, num = 1

printf @"%d rows:", rows
for row = 1 to rows
for col = 1 to row
printf @"%4d\b", num
num++
next
print
next
print
end fn

fn FloydsTriangle(  5 )
fn FloydsTriangle( 14 )

HandleEvents```
Output:
```5 rows:
1
2   3
4   5   6
7   8   9  10
11  12  13  14  15

14 rows:
1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

## Gambas

```Public Sub Main()
Dim siCount, siNo, siCounter As Short
Dim siLine As Short = 1
Dim siInput As Short[] = [5, 14]

For siCount = 0 To siInput.Max
Print "Floyd's triangle to " & siInput[siCount] & " lines"
Do
Inc siNo
Inc siCounter
Print Format(siNo, "####");
If siLine = siCounter Then
Print
Inc siLine
siCounter = 0
End If
If siLine - 1 = siInput[siCount] Then Break
Loop
siLine = 1
siCounter = 0
siNo = 0
Print
Next

End```

Output:

```Floyd's triangle to 5 lines
1
2   3
4   5   6
7   8   9  10
11  12  13  14  15

Floyd's triangle to 14 lines
1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

## Go

```package main

import "fmt"

func main() {
floyd(5)
floyd(14)
}

func floyd(n int) {
fmt.Printf("Floyd %d:\n", n)
lowerLeftCorner := n*(n-1)/2 + 1
lastInColumn := lowerLeftCorner
lastInRow := 1
for i, row := 1, 1; row <= n; i++ {
w := len(fmt.Sprint(lastInColumn))
if i < lastInRow {
fmt.Printf("%*d ", w, i)
lastInColumn++
} else {
fmt.Printf("%*d\n", w, i)
row++
lastInRow += row
lastInColumn = lowerLeftCorner
}
}
}
```
Output:
```Floyd 5:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
Floyd 14:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Groovy

Translation of: Java
```class Floyd {
static void main(String[] args) {
printTriangle(5)
printTriangle(14)
}

private static void printTriangle(int n) {
println(n + " rows:")
int printMe = 1
int numsPrinted = 0
for (int rowNum = 1; rowNum <= n; printMe++) {
int cols = (int) Math.ceil(Math.log10(n * (n - 1) / 2 + numsPrinted + 2))
printf("%" + cols + "d ", printMe)
if (++numsPrinted == rowNum) {
println()
rowNum++
numsPrinted = 0
}
}
}
}
```
Output:
```5 rows:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
14 rows:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

```--------------------- FLOYDS TRIANGLE --------------------

floydTriangle :: [[Int]]
floydTriangle =
( zipWith
(fmap (.) enumFromTo <*> (\a b -> pred (a + b)))
<\$> scanl (+) 1
<*> id
)
[1 ..]

--------------------------- TEST -------------------------
main :: IO ()
main = mapM_ (putStrLn . formatFT) [5, 14]

------------------------- DISPLAY ------------------------

formatFT :: Int -> String
formatFT n = unlines \$ unwords . zipWith alignR ws <\$> t
where
t = take n floydTriangle
ws = length . show <\$> last t

alignR :: Int -> Int -> String
alignR n =
( (<>)
=<< flip replicate ' '
. (-) n
. length
)
. show
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

Or, simplifying a little by delegating the recursion scheme to mapAccumL

```import Control.Monad ((>=>))
import Data.List (mapAccumL)

--------------------- FLOYD'S TRIANGLE -------------------

floyd :: Int -> [[Int]]
floyd n =
snd \$
mapAccumL
(\a x -> ((,) . succ <*> enumFromTo a) (a + x))
1
[0 .. pred n]

--------------------------- TEST -------------------------
main :: IO ()
main = mapM_ putStrLn \$ showFloyd . floyd <\$> [5, 14]

showFloyd :: [[Int]] -> String
showFloyd x =
let padRight n = (drop . length) <*> (replicate n ' ' <>)
in unlines
( fmap
( zipWith
(\n v -> padRight n (show v))
(fmap (succ . length . show) (last x))
>=> id
)
x
)
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

Or, defining just the relationship between successive terms:

```----------------- LINES OF FLOYDS TRIANGLE ---------------

floyds :: [[Int]]
floyds = iterate floyd [1]

floyd :: [Int] -> [Int]
floyd xs
| n < 2 = [1]
| otherwise =
[ succ (div (n * pred n) 2)
.. div (n * succ n) 2
]
where
n = succ (length xs)

--------------------------- TEST -------------------------
main :: IO ()
main = do
mapM_ print \$ take 5 floyds
putStrLn ""
mapM_ print \$ take 14 floyds
```
Output:
```[1]
[2,3]
[4,5,6]
[7,8,9,10]
[11,12,13,14,15]

[1]
[2,3]
[4,5,6]
[7,8,9,10]
[11,12,13,14,15]
[16,17,18,19,20,21]
[22,23,24,25,26,27,28]
[29,30,31,32,33,34,35,36]
[37,38,39,40,41,42,43,44,45]
[46,47,48,49,50,51,52,53,54,55]
[56,57,58,59,60,61,62,63,64,65,66]
[67,68,69,70,71,72,73,74,75,76,77,78]
[79,80,81,82,83,84,85,86,87,88,89,90,91]
[92,93,94,95,96,97,98,99,100,101,102,103,104,105]```

Or as a partially populated matrix:

```import Control.Monad (join)
import Data.Matrix (Matrix, getElem, matrix, nrows, toLists)

--------------------- FLOYDS TRIANGLE --------------------

floyd :: Int -> Matrix (Maybe Int)
floyd n = matrix n n go
where
go (y, x)
| x > y = Nothing
| otherwise = Just (x + quot (pred y * y) 2)

--------------------------- TEST -------------------------
main :: IO ()
main = mapM_ putStrLn \$ showFloyd . floyd <\$> [5, 14]

------------------------- DISPLAY ------------------------

showFloyd :: Matrix (Maybe Int) -> String
showFloyd m =
(unlines . fmap unwords . toLists) \$
go <\$> m
where
go Nothing = ""
go (Just n) = padRight w (show n)
Just v = join getElem (nrows m) m
w = length (show v)

padRight :: Int -> String -> String
padRight n = (drop . length) <*> (replicate n ' ' <>)
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105```

## Icon and Unicon

The following solution works in both languages:

```procedure main(a)
n := integer(a[1]) | 5
w := ((n*(n-1))/2)-n
c := create seq()
every row := 1 to n do {
every col := 1 to row do {
width := *(w+col)+1
every writes(right(@c,width))
}
write()
}
end
```

Sample outputs:

```->ft
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
->
```
```->ft 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
->
```

## J

Note: `require 'strings'` does nothing in J7, but is harmless (strings is already incorporated in J7).

```require 'strings'
floyd=: [: rplc&(' 0';'  ')"1@":@(* (\$ \$ +/\@,)) >:/~@:i.
```

Note, the parenthesis around (\$ \$ +/\@,) is optional, and only included for emphasis.

Example use:

```   floyd 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
floyd 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

How it works:

First, we create a square lower triangular matrix with our argument as the length of one side. We have 1s along the diagonal and the lower triangle, and 0s for the upper triangle.

Second, we create a running sum of these values (treating rows as being adjacent horizontally for this purpose). Then, we multiply this result by our lower triangular matrix (forcing the upper triangle to be 0s).

Then, we format the matrix as text (which gives us the required vertical alignment), and in each row we replace each space followed by a zero with two spaces.

Efficiency note: In a measurement of time used: in floyd 100, 80% the time here goes into the string manipulations -- sequential additions and multiplications are cheap. In floyd 1000 this jumps to 98% of the time. Here's a faster version (about 3x on floyd 1000) courtesy of Aai of the J forums:

```floyd=: [: ({.~ i.&1@E.~&' 0')"1@":@(* (\$ \$ +/\@,)) >:/~@:i.
```

## Java

```public class Floyd {
public static void main(String[] args){
printTriangle(5);
printTriangle(14);
}

private static void printTriangle(int n){
System.out.println(n + " rows:");
for(int rowNum = 1, printMe = 1, numsPrinted = 0;
rowNum <= n; printMe++){
int cols = (int)Math.ceil(Math.log10(n*(n-1)/2 + numsPrinted + 2));
System.out.printf("%"+cols+"d ", printMe);
if(++numsPrinted == rowNum){
System.out.println();
rowNum++;
numsPrinted = 0;
}
}
}
}
```

Output:

```5 rows:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
14 rows:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

## JavaScript

### ES5

(In a functional idiom of JavaScript)

Two main functions:

1. An expression of the Floyd triangle as a list of lists (a function of the number of rows),
2. and a mapping of that expression to a formatted string.
```(function () {
'use strict';

// FLOYD's TRIANGLE -------------------------------------------------------

// floyd :: Int -> [[Int]]
function floyd(n) {
return snd(mapAccumL(function (start, row) {
return [start + row + 1, enumFromTo(start, start + row)];
}, 1, enumFromTo(0, n - 1)));
};

// showFloyd :: [[Int]] -> String
function showFloyd(xss) {
var ws = map(compose([succ, length, show]), last(xss));
return unlines(map(function (xs) {
return concat(zipWith(function (w, x) {
return justifyRight(w, ' ', show(x));
}, ws, xs));
}, xss));
};

// GENERIC FUNCTIONS ------------------------------------------------------

// compose :: [(a -> a)] -> (a -> a)
function compose(fs) {
return function (x) {
return fs.reduceRight(function (a, f) {
return f(a);
}, x);
};
};

// concat :: [[a]] -> [a] | [String] -> String
function concat(xs) {
if (xs.length > 0) {
var unit = typeof xs[0] === 'string' ? '' : [];
return unit.concat.apply(unit, xs);
} else return [];
};

// enumFromTo :: Int -> Int -> [Int]
function enumFromTo(m, n) {
return Array.from({
length: Math.floor(n - m) + 1
}, function (_, i) {
return m + i;
});
};

// justifyRight :: Int -> Char -> Text -> Text
function justifyRight(n, cFiller, strText) {
return n > strText.length ? (cFiller.repeat(n) + strText)
.slice(-n) : strText;
};

// last :: [a] -> a
function last(xs) {
return xs.length ? xs.slice(-1)[0] : undefined;
};

// length :: [a] -> Int
function length(xs) {
return xs.length;
};

// map :: (a -> b) -> [a] -> [b]
function map(f, xs) {
return xs.map(f);
};

// 'The mapAccumL function behaves like a combination of map and foldl;
// it applies a function to each element of a list, passing an accumulating
// parameter from left to right, and returning a final value of this
// accumulator together with the new list.' (See hoogle )

// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
function mapAccumL(f, acc, xs) {
return xs.reduce(function (a, x) {
var pair = f(a[0], x);

return [pair[0], a[1].concat([pair[1]])];
}, [acc, []]);
};

// show ::
// (a -> String) f,  Num n =>
// a -> maybe f -> maybe n -> String
var show = JSON.stringify;

// snd :: (a, b) -> b
function snd(tpl) {
return Array.isArray(tpl) ? tpl[1] : undefined;
};

// succ :: Int -> Int
function succ(x) {
return x + 1;
};

// unlines :: [String] -> String
function unlines(xs) {
return xs.join('\n');
};

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
function zipWith(f, xs, ys) {
var ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map(function (x, i) {
return f(x, ys[i]);
});
};

// TEST ( n=5 and n=14 rows ) ---------------------------------------------

return unlines(map(function (n) {
return showFloyd(floyd(n)) + '\n';
}, [5, 14]));
})();
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

### ES6

(mapAccumL version)

```(() => {
'use strict';

// FLOYD's TRIANGLE -------------------------------------------------------

// floyd :: Int -> [[Int]]
const floyd = n => snd(mapAccumL(
(start, row) => [start + row + 1, enumFromTo(start, start + row)],
1, enumFromTo(0, n - 1)
));

// showFloyd :: [[Int]] -> String
const showFloyd = xss => {
const ws = map(compose([succ, length, show]), last(xss));
return unlines(
map(xs => concat(zipWith(
(w, x) => justifyRight(w, ' ', show(x)), ws, xs
)),
xss
)
);
};

// GENERIC FUNCTIONS ------------------------------------------------------

// compose :: [(a -> a)] -> (a -> a)
const compose = fs => x => fs.reduceRight((a, f) => f(a), x);

// concat :: [[a]] -> [a] | [String] -> String
const concat = xs => {
if (xs.length > 0) {
const unit = typeof xs[0] === 'string' ? '' : [];
return unit.concat.apply(unit, xs);
} else return [];
};

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = (m, n) =>
Array.from({
length: Math.floor(n - m) + 1
}, (_, i) => m + i);

// justifyRight :: Int -> Char -> Text -> Text
const justifyRight = (n, cFiller, strText) =>
n > strText.length ? (
(cFiller.repeat(n) + strText)
.slice(-n)
) : strText;

// last :: [a] -> a
const last = xs => xs.length ? xs.slice(-1)[0] : undefined;

// length :: [a] -> Int
const length = xs => xs.length;

// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f)

// 'The mapAccumL function behaves like a combination of map and foldl;
// it applies a function to each element of a list, passing an accumulating
// parameter from left to right, and returning a final value of this
// accumulator together with the new list.' (See hoogle )

// mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
const mapAccumL = (f, acc, xs) =>
xs.reduce((a, x) => {
const pair = f(a[0], x);

return [pair[0], a[1].concat([pair[1]])];
}, [acc, []]);

// show ::
// (a -> String) f,  Num n =>
// a -> maybe f -> maybe n -> String
const show = JSON.stringify;

// snd :: (a, b) -> b
const snd = tpl => Array.isArray(tpl) ? tpl[1] : undefined;

// succ :: Int -> Int
const succ = x => x + 1

// unlines :: [String] -> String
const unlines = xs => xs.join('\n');

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) => {
const ny = ys.length;
return (xs.length <= ny ? xs : xs.slice(0, ny))
.map((x, i) => f(x, ys[i]));
};

// TEST ( n=5 and n=14 rows ) ---------------------------------------------

return unlines(map(n => showFloyd(floyd(n)) + '\n', [5, 14]))
})();
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

### Spidermonkey

(Used TCL example as a starting point.)

```#!/usr/bin/env js

function main() {
print('Floyd 5:');
floyd(5);
print('\nFloyd 14:');
floyd(14);
}

for (s = String(s); s.length < w; s = ' ' + s);
return s;
}

function floyd(nRows) {
var lowerLeft = nRows * (nRows - 1) / 2 + 1;
var lowerRight = nRows * (nRows + 1) / 2;

var colWidths = [];
for (var col = lowerLeft; col <= lowerRight; col++) {
colWidths.push(String(col).length);
}

var  num = 1;
for (var row = 0; row < nRows; row++) {
var line = [];
for (var col = 0; col <= row; col++, num++) {
}
print(line.join(' '));
}
}

main();
```
Output:
``` Floyd 5:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

Floyd 14:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## jq

```# floyd(n) creates an n-row floyd's triangle
def floyd(n):
def lpad(len): tostring | (((len - length) * " ")  + .);

# Construct an array of widths.
# Assuming N is the last integer on the last row (i.e. (n+1)*n/2),
# the last row has n entries from (1+N-n) through N:
def widths:
((n+1)*n/2) as \$N
| [range(1 + \$N - n; \$N + 1) | tostring | length];

# emit line k assuming it starts with the integer "start"
def line(start; k; widths):
reduce range(start; start+k) as \$i
(""; . + (\$i|lpad(widths[\$i - start])) + " ");

widths as \$widths
| (reduce range(0;n) as \$row
( [0, ""];   # state: i, string
(.[0] + 1) as \$i | .[1] as \$string
| [ (\$i + \$row),
(\$string + "\n" + line(\$i; \$row + 1; \$widths )) ] )
| .[1] ) ;```

`(5,14) | "floyd(\(.)): \(floyd(.))\n"`
Output:
```\$ jq -M -r -n -f floyds_triangle.jq > floyds_triangle.out
floyd(5):
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

floyd(14):
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Julia

```function floydtriangle(rows)
r = collect(1:div(rows *(rows + 1), 2))
for i in 1:rows
for j in 1:i
print(rpad(lpad(popfirst!(r), j > 8 ? 3 : 2), j > 8 ? 4 : 3))
end
println()
end
end

floydtriangle(5); println(); floydtriangle(14)
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Kotlin

Translation of: Java
```fun main(args: Array<String>) = args.forEach { Triangle(it.toInt()) }

internal class Triangle(n: Int) {
init {
println("\$n rows:")
var printMe = 1
var printed = 0
var row = 1
while (row <= n) {
val cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0)).toInt()
print("%\${cols}d ".format(printMe))
if (++printed == row) { println(); row++; printed = 0 }
printMe++
}
}
}
```

Output as Java.

## Lasso

 This example does not show the output mentioned in the task description on this page (or a page linked to from here). There should only be one space between the numbers on the last row. Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.

```define floyds_triangle(n::integer) => {
local(out = array(array(1)),comp = array, num = 1)
while(#out->size < #n) => {
local(new = array)
loop(#out->last->size + 1) => {
#num++
#new->insert(#num)
}
#out->insert(#new)
}
with line in #out do => {
local(lineout = string)
with i in #line do => {
#i != #line->first ? #lineout->append(' ')
}
#comp->insert(#lineout)
}
return #comp->join('\r')
}
floyds_triangle(5)
'\r\r'
floyds_triangle(14)
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105```

## Liberty BASIC

```input "Number of rows needed:- "; rowsNeeded

dim colWidth(rowsNeeded)    '    5 rows implies 5 columns

for col=1 to rowsNeeded
colWidth(col) = len(str\$(col + rowsNeeded*(rowsNeeded-1)/2))
next

currentNumber =1

for row=1 to rowsNeeded
for col=1 to row
print right\$( "  "+str\$( currentNumber), colWidth(col)); " ";
currentNumber = currentNumber + 1
next
print
next```
Output:
```Number of rows needed:- 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

Number of rows needed:- 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

## Lua

```function print_floyd(rows)
local c = 1
local h = rows*(rows-1)/2
for i=1,rows do
local s = ""
for j=1,i do
for k=1, #tostring(h+j)-#tostring(c) do
s = s .. " "
end
if j ~= 1 then s = s .. " " end
s = s .. tostring(c)
c = c + 1
end
print(s)
end
end

print_floyd(5)
print_floyd(14)
```

Output:

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Maple

```floyd := proc(rows)
local num, numRows, numInRow, i, digits;
digits := Array([]);
for i to 2 do
num := 1;
numRows := 1;
numInRow := 1;
while numRows <= rows do
if i = 2 then
printf(cat("%", digits[numInRow], "a "), num);
end if;
num := num + 1;
if i = 1 and numRows = rows then
digits(numInRow) := StringTools[Length](convert(num-1, string));
end if;
if numInRow >= numRows then
if i = 2 then
printf("\n");
end if;
numInRow := 1;
numRows := numRows + 1;
else
numInRow := numInRow +1;
end if;
end do;
end do;
return NULL;
end proc:

floyd(5);
floyd(14);```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Mathematica / Wolfram Language

```f=Function[n,
Most/@(Range@@@Partition[FindSequenceFunction[{1,2,4,7,11}]/@Range[n+1],2,1])]
TableForm[f@5,TableAlignments->Right,TableSpacing->{1,1}]
TableForm[f@14,TableAlignments->Right,TableSpacing->{1,1}]
```

Output:

```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## MATLAB / Octave

```function floyds_triangle(n)
s = 1;
for k = 1 : n
disp(s : s + k - 1)
s = s + k;
end
```
Output:
```octave:22> floyds_triangle(5)
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```

## Maxima

```floyd_t(m):=block(
t:m*(m+1)/2,
L1:makelist(makelist(k,k,1,t),j,0,m),
L2:makelist(rest(L1[i],((i-1)^2+(i-1))/2),i,1,m+1),
makelist(firstn(L2[i],i),i,1,m),
table_form(%%))\$

/* Test cases */
floyd_t(5);
floyd_t(14);
```

## Miranda

```main :: [sys_message]
main = [Stdout (lay (map floyd [5, 14]))]

floyd :: num->[char]
floyd n = lay (map fmt rws)
where rws = rows n
cws = map ((+1).width) (last rws)
fmt rw = concat (map (uncurry rjust) (zip2 cws rw))

rows :: num->[[num]]
rows n = rows' [1..n] [1..]
where rows' []     ns = []
rows' (l:ls) ns = row : rows' ls rest
where (row, rest) = split l ns

split :: num->[*]->([*],[*])
split n ls = (take n ls, drop n ls)

rjust :: num->num->[char]
rjust w n = reverse (take w (reverse (show n) ++ repeat ' '))

width :: num->num
width = (#) . show

uncurry :: (*->**->***)->(*,**)->***
uncurry f (a,b) = f a b```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Modula-2

```MODULE FloydTriangle;
FROM FormatString IMPORT FormatString;

PROCEDURE WriteInt(n : INTEGER);
VAR buf : ARRAY[0..9] OF CHAR;
BEGIN
FormatString("%4i", buf, n);
WriteString(buf)
END WriteInt;

PROCEDURE Print(r : INTEGER);
VAR n,i,limit : INTEGER;
BEGIN
IF r<0 THEN RETURN END;

n := 1;
limit := 1;
WHILE r#0 DO
FOR i:=1 TO limit DO
WriteInt(n);
INC(n)
END;
WriteLn;

DEC(r);
INC(limit)
END
END Print;

BEGIN
Print(5);
WriteLn;
Print(14);

END FloydTriangle.
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## NetRexx

Both REXX versions lend themselves very well to conversion into NetRexx programs with few changes.

### Version 1

Translation of: REXX
```/* NetRexx */
options replace format comments java crossref symbols binary
/* REXX ***************************************************************
* 12.07.2012 Walter Pachl  - translated from Python
**********************************************************************/
Parse Arg rowcount .
if rowcount.length() == 0 then rowcount = 1
say 'Rows:' rowcount
say
col = 0
len = Rexx ''
ll = ''                               -- last line of triangle
Loop j = rowcount * (rowcount - 1) / 2 + 1 to rowcount * (rowcount + 1) / 2
col = col + 1                       -- column number
ll = ll j                           -- build last line
len[col] = j.length()               -- remember length of column
End j
Loop i = 1 To rowcount - 1            -- now do and output the rest
ol = ''
col = 0
Loop j = i * (i - 1) / 2 + 1 to i * (i + 1) / 2 -- elements of line i
col = col + 1
ol=ol j.right(len[col])           -- element in proper length
end
Say ol                              -- output ith line
end i
Say ll                                -- output last line```

Output:

```Rows: 5

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

Rows: 14

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

### Version 2

Translation of: REXX
```/* NetRexx */
options replace format comments java crossref symbols binary
/*REXX program constructs & displays Floyd's triangle for any number of rows.*/
parse arg numRows .
if numRows == '' then numRows = 1     -- assume 1 row if not given
maxVal = numRows * (numRows + 1) % 2  -- calculate the max value.
say 'displaying a' numRows "row Floyd's triangle:"
say
digit = 1
loop row = 1 for numRows
col = 0
output = ''
loop digit = digit for row
col = col + 1
colMaxDigit = maxVal - numRows + col
output = output Rexx(digit).right(colMaxDigit.length())
end digit
say output
end row```

Output:

```displaying a 5 row Floyd's triangle:

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

displaying a 14 row Floyd's triangle:

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Nim

Translation of: Python
```import strutils

proc floyd(rowcount = 5): seq[seq[int]] =
result = @[@[1]]
while result.len < rowcount:
let n = result[result.high][result.high] + 1
var row = newSeq[int]()
for i in n .. n + result[result.high].len:

proc pfloyd(rows: seq[seq[int]]) =
var colspace = newSeq[int]()
for row in rows:
for i, x in row:
stdout.write align(\$x, colspace[i])," "
echo ""

for i in [5, 14]:
pfloyd(floyd(i))
echo ""
```

Output:

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

## OCaml

```let ( |> ) f g x = g (f x)
let rec last = function x::[] -> x | _::tl -> last tl | [] -> raise Not_found
let rec list_map2 f l1 l2 =
match (l1, l2) with
| ([], _) | (_, []) -> []
| (x::xs, y::ys) -> (f x y) :: list_map2 f xs ys

let floyd n =
let rec aux acc cur len i j =
if (List.length acc) = n then (List.rev acc) else
if j = len
then aux ((List.rev cur)::acc) [] (succ len) i 0
else aux acc (i::cur) len (succ i) (succ j)
in
aux [] [] 1 1 0

let print_floyd f =
let lens = List.map (string_of_int |> String.length) (last f) in
List.iter (fun row ->
print_endline (
String.concat " " (
list_map2 (Printf.sprintf "%*d") lens row))
) f

let () =
print_floyd (floyd (int_of_string Sys.argv.(1)))
```

## OxygenBasic

 This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.

```function Floyd(sys n) as string
sys i,t
for i=1 to n
t+=i
next
string s=str t
sys le=1+len s
string cr=chr(13,10)
sys lc=len cr
string buf=space(le*t+n*lc)
sys j,o,p=1
t=0
for i=1 to n
for j=1 to i
t++
s=str t
o=le-len(s)-1 'right justify
mid buf,p+o,str t
p+=le
next
mid buf,p,cr
p+=lc
next
return left buf,p-1
end function

putfile "s.txt",Floyd(5)+floyd(14)```

## PARI/GP

```{floyd(m)=my(lastrow_a,lastrow_e,lastrow_len=m,fl,idx);
\\ +++  fl is a vector of fieldlengths in the last row
lastrow_e=m*(m+1)/2;lastrow_a=lastrow_e+1-m;
fl=vector(lastrow_len);
for(k=1,m,fl[k] = 1 + #Str(k-1+lastrow_a) );
\\
idx=0;
for(i=1,m,
for(j=1,i,
idx++;
printf(Str("%" fl[j] "d"),idx)
);
print()
);
return();}
floyd(5)
floyd(14)```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Pascal

Works with: Free_Pascal
```Program FloydDemo (input, output);

function digits(number: integer): integer;
begin
digits := trunc(ln(number) / ln(10)) + 1;
end;

procedure floyd1 (numberOfLines: integer);
{ variant with repeat .. until loop }
var
i, j, numbersInLine, startOfLastlLine: integer;

begin
startOfLastlLine := (numberOfLines - 1) * numberOfLines div 2 + 1;
i := 1;
j := 1;
numbersInLine := 1;
repeat
repeat
write(i: digits(startOfLastlLine - 1 + j), ' ');
inc(i);
inc(j);
until (j > numbersInLine);
writeln;
j := 1;
inc(numbersInLine);
until (numbersInLine > numberOfLines);
end;

procedure floyd2 (numberOfLines: integer);
{ Variant with for .. do loop }
var
i, j, numbersInLine, startOfLastlLine: integer;

begin
startOfLastlLine := (numberOfLines - 1) * numberOfLines div 2 + 1;
i := 1;
for numbersInLine := 1 to numberOfLines do
begin
for j := 1 to numbersInLine do
begin
write(i: digits(startOfLastlLine - 1 + j), ' ');
inc(i);
end;
writeln;
end;
end;

begin
writeln ('*** Floyd 5 ***');
floyd1(5);
writeln;
writeln ('*** Floyd 14 ***');
floyd2(14);
end.
```

Output:

```% ./Floyd
*** Floyd 5 ***
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

*** Floyd 14 ***
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

## PascalABC.NET

```procedure FloydTriangle(rows: integer);
begin
var r := 1;
for var i:=1 to rows do
begin
for var j:=1 to i do
begin
Write(r: (j>8 ? 4 : 3));
r += 1;
end;
Writeln
end;
end;

begin
FloydTriangle(5);
Writeln;
FloydTriangle(14);
end.
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Perl

Translation of: NetRexx
```#!/usr/bin/env perl
use strict;
use warnings;

sub displayFloydTriangle {
my \$numRows = shift;
print "\ndisplaying a \$numRows row Floyd's triangle:\n\n";
my \$maxVal = int(\$numRows * (\$numRows + 1) / 2); # calculate the max value.
my \$digit = 0;
foreach my \$row (1 .. \$numRows) {
my \$col = 0;
my \$output = '';
foreach (1 .. \$row) {
++\$digit;
++\$col;
my \$colMaxDigit = \$maxVal - \$numRows + \$col;
\$output .= sprintf " %*d", length(\$colMaxDigit), \$digit;
}
print "\$output\n";
}
return;
}

# ==== Main ================================================
my @counts;
@counts = @ARGV;
@counts = (5, 14) unless @ARGV;

foreach my \$count (@counts) {
displayFloydTriangle(\$count);
}

0;
__END__
```

Output:

```displaying a 5 row Floyd's triangle:

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

displaying a 14 row Floyd's triangle:

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Phix

```with javascript_semantics
procedure Floyds_triangle(integer n)
sequence widths = repeat(0,n)
integer k = (n * (n-1))/2
for i=1 to n do
widths[i] = sprintf("%%%dd",length(sprintf("%d",i+k))+1)
end for
k = 1
for i=1 to n do
for j=1 to i do
printf(1,widths[j],k)
k += 1
end for
printf(1,"\n")
end for
end procedure
Floyds_triangle(5)
Floyds_triangle(14)
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## PHP

```<?php
floyds_triangle(5);
floyds_triangle(14);

function floyds_triangle(\$n) {
echo "n = " . \$n . "\r\n";

for(\$r = 1, \$i = 1, \$c = 0; \$r <= \$n; \$i++) {
\$cols = ceil(log10(\$n*(\$n-1)/2 + \$c + 2));
printf("%".\$cols."d ", \$i);
if(++\$c == \$r) {
echo "\r\n";
\$r++;
\$c = 0;
}
}
?>
```
Output:
```
n = 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
n = 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Picat

### List comprehension

```import util.

% Calculate the numbers first and then format them
floyd1(N) = S =>
M = [[J+SS : J in 1..I] : I in 1..N, SS=sum(1..I-1)],
S = [slice(SS,2) : Row in M, SS = [to_fstring(to_fstring("%%%dd",M[N,I].to_string().length+1),E) :
{E,I} in zip(Row,1..Row.length)].join('')].join("\n").```

### Loop based

Translation of: Prolog

Picat doesn't support all of SWI-Prolog's nifty format options so we have to tweak a bit.

```floyd2(N) = S =>
S = [],
foreach(I in 1..N)
SS = "",
foreach(J in 1..I)
Last = N * (N-1)/2+J,
V = I * (I-1) // 2 + J,
C = Last.to_string().length-1,
SS := SS ++ to_fstring(to_fstring("%%%dd",C), V)
end,
S := S ++ slice(SS,2) ++ "\n"
end.```

### Test

```go =>
println("N=5:"),
println(floyd1(5)),
nl,
println("N=14:"),
println(floyd2(14)),
nl.```
Output:
```N=5:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

N=14:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## PicoLisp

### Calculate widths relative to lower left corner

```(de floyd (N)
(let LLC (/ (* N (dec N)) 2)
(for R N
(for C R
(prin
(align
(length (+ LLC C))
(+ C (/ (* R (dec R)) 2)) ) )
(if (= C R) (prinl) (space)) ) ) ) )```

### Pre-calculate all rows, and take format from last one

```(de floyd (N)
(let
(Rows
(make
(for ((I . L) (range 1 (/ (* N (inc N)) 2))  L)
(link (cut I 'L)) ) )
Fmt (mapcar length (last Rows)) )
(map inc (cdr Fmt))
(for R Rows
(apply tab R Fmt) ) ) )```

Output in both cases:

```: (floyd 5)
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

: (floyd 14)
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## PL/I

```(fofl, size):
floyd: procedure options (main); /* Floyd's Triangle. Wiki 12 July 2012 */

declare (i, m, n) fixed (10), (j, k, w, nr) fixed binary;

put list ('How many rows do you want?');
get list (nr);   /* the number of rows   */
n = nr*(nr+1)/2; /* the total number of values */

j,k = 1; m = n - nr + 1;
do i = 1 to n;
put edit (i) ( x(1), f(length(trim(m))) );
if k > 1 then do; k = k - 1; m = m + 1; end;
else do; k,j = j + 1; m = n - nr + 1; put skip; end;
end;

end floyd;```
Output:
```How many rows do you want?
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

How many rows do you want?
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105

Final row for n=45:
991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
```

## PL/M

```100H:
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; GO TO 0; END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;

PUT\$NUM: PROCEDURE (N, WIDTH);
DECLARE S (6) BYTE INITIAL ('     \$');
DECLARE N ADDRESS, (I, WIDTH) BYTE;
I = 5;
DIGIT:
S(I := I-1) = N MOD 10 + '0';
IF (N := N/10) > 0 THEN GO TO DIGIT;
DO I=I-1 TO 0 BY -1;
S(I) = ' ';
END;
CALL PRINT(.S(6-WIDTH));
END PUT\$NUM;

WIDTH: PROCEDURE (N) BYTE;
DECLARE (N, W) BYTE;
W = 1;
DO WHILE N>0;
N = N/10;
W = W+1;
END;
RETURN W;
END WIDTH;

FLOYD: PROCEDURE (ROWS);
DECLARE (ROWS, ROW, COL) BYTE;

MAXNO = ROWS * (ROWS+1)/2;
N = 1;
DO ROW = 1 TO ROWS;
DO COL = 1 TO ROW;
CALL PUT\$NUM(N, 1 + WIDTH(MAXNO - ROWS + COL));
N = N+1;
END;
CALL PRINT(.(13,10,'\$'));
END;
END FLOYD;

CALL FLOYD(5);
CALL PRINT(.(13,10,'\$'));
CALL FLOYD(14);
CALL EXIT;
EOF```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

11
12 13
14 15 16
17 18 19 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Prolog

Works with SWI-Prolog version 6.5.3

```floyd(N) :-
forall(between(1, N, I),
(   forall(between(1,I, J),
(   Last is N * (N-1)/2+J,
V is I * (I-1) /2 + J,
get_column(Last, C),
sformat(AR, '~~t~~w~~~w| ', [C]),
sformat(AF, AR, [V]),
writef(AF))),
nl)).

get_column(Last, C) :-
name(Last, N1), length(N1,C).
```

Output :

``` ?- floyd(5).
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
true.

?- floyd(14).
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
true.
```

## PureBasic

```Procedure.i sumTo(n)
Protected r,i
For i=1 To n
r+i
Next
ProcedureReturn r.i
EndProcedure

; [1]
; array rsA(n)... string-lengths of the numbers
; in the bottom row

; [2]
; sumTo(i-1)+1    to     sumTo(i)
; 11 12 13 14 15
; here k is the column-index for array rsA(k)

Procedure.s FloydsTriangle(n)
Protected r.s,s.s,t.s,i,j,k
; [1]
Dim rsA(n)
i=0
For j=sumTo(n-1)+1 To sumTo(n)
i+1
rsA(i)=Len(Str(j))
Next
; [2]
For i=1 To n
t.s="":k=0
For j=sumTo(i-1)+1 To sumTo(i)
k+1:t.s+RSet(Str(j),rsA(k)," ")+" "
Next
r.s+RTrim(t.s)+Chr(13)+Chr(10)
Next
r.s=Left(r.s,Len(r.s)-2)
ProcedureReturn r.s
EndProcedure

If OpenConsole()
n=5
r.s=FloydsTriangle(n)
PrintN(r.s)

n=14
r.s=FloydsTriangle(n)
PrintN(r.s)

Print(#crlf\$ + #crlf\$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf```

Sample Output

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Python

### Procedural

```>>> def floyd(rowcount=5):
rows = [[1]]
while len(rows) < rowcount:
n = rows[-1][-1] + 1
rows.append(list(range(n, n + len(rows[-1]) + 1)))
return rows

>>> floyd()
[[1], [2, 3], [4, 5, 6], [7, 8, 9, 10], [11, 12, 13, 14, 15]]
>>> def pfloyd(rows=[[1], [2, 3], [4, 5, 6], [7, 8, 9, 10]]):
colspace = [len(str(n)) for n in rows[-1]]
for row in rows:
print( ' '.join('%*i' % space_n for space_n in zip(colspace, row)))

>>> pfloyd()
1
2 3
4 5 6
7 8 9 10
>>> pfloyd(floyd(5))
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
>>> pfloyd(floyd(14))
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
>>>
```

### Functional

Using the mathematical formula for each row directly, either in a list comprehension:

```def floyd(rowcount=5):
return [list(range(i * (i - 1) // 2 + 1, i * (i + 1) // 2 + 1))
for i in range(1, rowcount + 1)]
```

or in terms of concatMap:

Works with: Python version 3
```'''Floyd triangle in terms of concatMap'''

from itertools import chain

# floyd :: Int -> [[Int]]
def floyd(n):
'''n rows of a Floyd triangle.'''
def f(i):
return [
enumFromTo(i * pred(i) // 2 + 1)(
i * succ(i) // 2
)
]
return concatMap(f)(enumFromTo(1)(n))

# main :: IO ()
def main():
'''Test'''
print(unlines(
map(str, floyd(5))
))

# GENERIC FUNCTIONS ---------------------------------------

# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))

# concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
'''Concatenated list over which a function has been mapped.
The list monad can be derived by using a function f which
wraps its output in a list,
(using an empty list to represent computational failure).'''
return lambda xs: list(
chain.from_iterable(
map(f, xs)
)
)

# pred ::  Enum a => a -> a
def pred(x):
'''The predecessor of a value. For numeric types, (- 1).'''
return x - 1 if isinstance(x, int) else (
chr(ord(x) - 1)
)

# succ :: Enum a => a -> a
def succ(x):
'''The successor of a value. For numeric types, (1 +).'''
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)

# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.'''
return '\n'.join(xs)

if __name__ == '__main__':
main()
```

Or alternatively, defining just the relationship between successive terms:

Works with: Python version 3
```'''Floyd triangle in terms of iterate(f)(x)'''

from itertools import islice

# floyd :: Int -> [[Int]]
def floyd(n):
'''n rows of a Floyd triangle.'''
return take(n)(iterate(nextFloyd)([1]))

# nextFloyd :: [Int] -> [Int]
def nextFloyd(xs):
'''A Floyd triangle row derived from
the preceding row.'''
n = succ(len(xs))
return [1] if n < 2 else (
enumFromTo(succ(n * pred(n) // 2))(
n * succ(n) // 2
)
)

# showFloyd :: [[Int]] -> String
def showFloyd(xs):
'''A stringification of Floyd triangle rows.'''
return unlines(str(x) for x in xs)

# main :: IO ()
def main():
'''Test'''
print(showFloyd(
floyd(5)
))

# GENERIC ABSTRACTIONS ------------------------------------

# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))

# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated applications of f to x.'''
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)

# pred ::  Enum a => a -> a
def pred(x):
'''The predecessor of a value. For numeric types, (- 1).'''
return x - 1 if isinstance(x, int) else (
chr(ord(x) - 1)
)

# succ :: Enum a => a -> a
def succ(x):
'''The successor of a value. For numeric types, (1 +).'''
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)

# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.'''
return lambda xs: (
xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
)

# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.'''
return '\n'.join(xs)

# MAIN ----------------------------------------------------
if __name__ == '__main__':
main()
```
Output:
```[1]
[2, 3]
[4, 5, 6]
[7, 8, 9, 10]
[11, 12, 13, 14, 15]```

## q

```floyd:{n:1+ til sum 1+til x;
t:d:0;
while[1+x-:1;0N!(t+:1)#(d+:t)_n]}

floyd2:{n:1+ til sum 1+til x;
t:d:0;
while[1+x-:1;1 (" " sv string each (t+:1)#(d+:t)_n),"\n"]}

//The latter function 'floyd2' includes logic to remove the leading "," before "1" in the first row.

floyd[5]
floyd2[14]
```
Output:
```,1
2 3
4 5 6
7 8 9 10
11 12 13 14 15

1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105

```

## Quackery

```  [ dup 1+ * 2 / ]       is triangulared (   n --> n )

[ number\$ tuck size -
times sp echo\$ ]     is rightecho    ( n n -->   )

[ dup triangulared
number\$ size 1+
0 rot times
[ i^ 1+ times
[ 1+ 2dup
rightecho ]
cr ]
2drop ]              is floyd        (   n -->   )

5 floyd
cr
14 floyd```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105

```

## R

If it weren't for the printing requirements, we could do this in one line.

```Floyd <- function(n)
{
#The first argument of the seq call is a well-known formula for triangle numbers.
out <- t(sapply(seq_len(n), function(i) c(seq(to = 0.5 * (i * (i + 1)), by = 1, length.out = i), rep(NA, times = n - i))))
dimnames(out) <- list(rep("", times = nrow(out)), rep("", times = ncol(out)))
print(out, na.print = "")
}
Floyd(5)
Floyd(14)```
Output:
```
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Racket

```#lang racket
(require math)

(define (tri n)
(if (zero? n) 0 (triangle-number n)))

(define (floyd n)
(define (width x) (string-length (~a x)))
(define (~n x c) (~a x
#:width (width (+ (tri (- n 1)) 1 c))
(for ([r n])
(for ([c (+ r 1)])
(display (~a (~n (+ (tri r) 1 c) c) " ")))
(newline)))

(floyd 5)
(floyd 14)
```

Output:

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Raku

(formerly Perl 6) Here's two ways of doing it.

```constant @floyd1 = (1..*).rotor(1..*);
constant @floyd2 = gather for 1..* -> \$s { take [++\$ xx \$s] }

sub format-rows(@f) {
my @table;
my @formats = @f[@f-1].map: {"%{.chars}s"}
for @f -> @row {
@table.push: (@row Z @formats).map: -> (\$i, \$f) { \$i.fmt(\$f) }
}
join "\n", @table;
}

say format-rows(@floyd1[^5]);
say '';
say format-rows(@floyd2[^14]);
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Refal

```\$ENTRY Go {
= <Prout <Floyd 5>>
<Prout <Floyd 14>>;
};

Floyd {
s.N, <Rows s.N>: e.Rows,
e.Rows: e.X (e.MaxRow),
<Each Width e.MaxRow>: e.ColWidths =
<Each ((e.ColWidths)) FormatRow e.Rows>;
}

FormatRow {
(e.W) () = '\n';
(s.W e.WS) (s.C e.CS) = <Cell <+ 1 s.W> s.C> <FormatRow (e.WS) (e.CS)>;
};

Cell {
s.Width s.N, <Repeat s.Width ' '> <Symb s.N>: e.Rfill,
<Last s.Width e.Rfill>: (e.X) e.Cell = e.Cell;
}

Rows {
s.Rows = <Rows s.Rows 1 1>;
s.Rows s.Row s.N, <+ s.Rows 1>: s.Row = ;
s.Rows s.Row s.N, <+ s.N s.Row>: s.Next =
(<Row s.N <- s.Next 1>>)
<Rows s.Rows <+ s.Row 1> s.Next>;
}

Row {
s.To s.To = s.To;
s.From s.To = s.From <Row <+ s.From 1> s.To>;
};

Each {
s.F e.X = <Each () s.F e.X>;
(e.Arg) s.F = ;
(e.Arg) s.F t.I e.X = <Mu s.F e.Arg t.I> <Each (e.Arg) s.F e.X>;
};

Width {
s.N, <Symb s.N>: e.X, <Lenw e.X>: s.Width e.X = s.Width;
};

Repeat {
0 s.X = ;
s.N s.X = s.X <Repeat <- s.N 1> s.X>;
};```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## REXX

### version 1

```
/* REXX ***************************************************************
* Parse Arg rowcount
* 12.07.2012 Walter Pachl  - translated from Python
**********************************************************************/
Parse Arg rowcount
col=0
ll=''                               /* last line of triangle         */
Do j=rowcount*(rowcount-1)/2+1 to rowcount*(rowcount+1)/2
col=col+1                         /* column number                 */
ll=ll j                           /* build last line               */
len.col=length(j)                 /* remember length of column     */
End
Do i=1 To rowcount-1                /* now do and output the rest    */
ol=''
col=0
Do j=i*(i-1)/2+1 to i*(i+1)/2     /* elements of line i            */
col=col+1
ol=ol right(j,len.col)          /* element in proper length      */
end
Say ol                            /* output ith line               */
end
Say ll                              /* output last line              */
```

Output:

```n=5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

n=14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

### version 2, simple formula

This REXX version uses a simple formula to calculate the maximum value (triangle element) displayed.

```/*REXX program constructs & displays  Floyd's triangle for any number of specified rows.*/
parse arg N .;    if N=='' | N==","  then N= 5   /*Not specified?  Then use the default.*/
mx= N * (N+1) % 2  - N                           /*calculate the maximum of any value.  */
say 'displaying a '  N  " row Floyd's triangle:" /*show the header for Floyd's triangle.*/
say                                              /*display a blank line below the title.*/
#=1;    do    r=1  for N;           i= 0;     _= /*construct Floyd's triangle row by row*/
do #=#  for r;           i= i + 1     /*start to construct a row of triangle.*/
_= _ right(#, length( mx+i ) )        /*build a row of the Floyd's triangle. */
end   /*#*/                           /*calculate the max length on the fly. */
say substr(_, 2)                         /*remove 1st leading blank in the line.*/
end      /*r*/                           /*stick a fork in it,  we're all done. */
```
output   when using the default input:
```displaying a  5  row Floyd's triangle:

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
```
output   when using the default input of:   14
```displaying a  14  row Floyd's triangle:

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```
output   (only showing the last row) when using the input of:   45
```  ··· 44 rows not shown ···
991  992  993  994  995  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
```

```/*REXX program constructs & displays Floyd's triangle for any number of rows in base 16.*/
parse arg N .;  if N=='' | N==","  then N=6      /*Not specified?  Then use the default.*/
mx=N * (N+1) % 2  -  N                           /*calculate maximum value of any value.*/
say 'displaying a '    N    " row Floyd's triangle in base 16:"  /*show triangle header.*/
say
#=1;  do     r=1  for N;     i=0;         _=     /*construct Floyd's triangle row by row*/
do #=#  for r;     i=i+1               /*start to construct a row of triangle.*/
_=_ right( d2x(#), length( d2x(mx+i))) /*build a row of the Floyd's triangle. */
end   /*#*/
say substr(_, 2)                           /*remove 1st leading blank in the line.*/
end       /*r*/                            /*stick a fork in it,  we're all done. */
```
output   when using the default input:
```displaying a  6  row Floyd's triangle in base 16:

1
2  3
4  5  6
7  8  9  A
B  C  D  E  F
10 11 12 13 14 15
```
output   when using the input of:   23
```displaying a  23  row Floyd's triangle in base 16:

1
2  3
4  5   6
7  8   9   A
B  C   D   E   F
10 11  12  13  14  15
16 17  18  19  1A  1B  1C
1D 1E  1F  20  21  22  23  24
25 26  27  28  29  2A  2B  2C  2D
2E 2F  30  31  32  33  34  35  36  37
38 39  3A  3B  3C  3D  3E  3F  40  41  42
43 44  45  46  47  48  49  4A  4B  4C  4D  4E
4F 50  51  52  53  54  55  56  57  58  59  5A  5B
5C 5D  5E  5F  60  61  62  63  64  65  66  67  68  69
6A 6B  6C  6D  6E  6F  70  71  72  73  74  75  76  77  78
79 7A  7B  7C  7D  7E  7F  80  81  82  83  84  85  86  87  88
89 8A  8B  8C  8D  8E  8F  90  91  92  93  94  95  96  97  98  99
9A 9B  9C  9D  9E  9F  A0  A1  A2  A3  A4  A5  A6  A7  A8  A9  AA  AB
AC AD  AE  AF  B0  B1  B2  B3  B4  B5  B6  B7  B8  B9  BA  BB  BC  BD  BE
BF C0  C1  C2  C3  C4  C5  C6  C7  C8  C9  CA  CB  CC  CD  CE  CF  D0  D1  D2
D3 D4  D5  D6  D7  D8  D9  DA  DB  DC  DD  DE  DF  E0  E1  E2  E3  E4  E5  E6  E7
E8 E9  EA  EB  EC  ED  EE  EF  F0  F1  F2  F3  F4  F5  F6  F7  F8  F9  FA  FB  FC  FD
FE FF 100 101 102 103 104 105 106 107 108 109 10A 10B 10C 10D 10E 10F 110 111 112 113 114
```

### version 4, up to base 90

This REXX version could be extended to even higher bases, all that is needed is to append more viewable characters to express "higher" numerals   ("digits" in base X).

This version of the base function has some boilerplate for signed numbers and various error checking.

```/*REXX program constructs/shows Floyd's triangle for any number of rows in any base ≤90.*/
parse arg N radx .                               /*obtain optional arguments from the CL*/
if    N=='' |    N==","  then    N= 5            /*Not specified?  Then use the default.*/
mx=N * (N+1) % 2  -  N                           /*calculate maximum value of any value.*/
say 'displaying a '  N   " row Floyd's triangle in base"  radx':'  /*display the header.*/
say
#=1;  do     r=1  for N;   i=0;            _=    /*construct Floyd's triangle row by row*/
do #=#  for r;    i=i+1                 /*start to construct a row of triangle.*/
end   /*#*/
say substr(_, 2)                           /*remove 1st leading blank in the line,*/
end      /*r*/                             /* [↑]   introduced by first abutment. */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
base: procedure; parse arg x 1 ox,toB,inB              /*obtain number, toBase, inBase. */
@abc= 'abcdefghijklmnopqrstuvwxyz'               /*lowercase Latin alphabet.      */
@abcU=@abc;        upper @abcU                   /*go whole hog and extend 'em.   */
@@@= '0123456789'@abc || @abcU                   /*prefix 'em with numeric digits.*/
@@@=@@@'<>[]{}()?~!@#\$%^&*_=|\/;:¢¬≈'            /*add some special chars as well.*/
/* [↑]  handles up to base 90,  all chars must be viewable.*/
numeric digits 3000                              /*what the hey, support gihugeics*/
mxB=length(@@@)                                  /*max base (radix) supported here*/
if toB=='' | toB=="," then toB=10                /*if skipped, assume default (10)*/
if inB=='' | inB=="," then inB=10                /* "    "        "      "      " */
if inB<2   | inb>mxB  then call erb 'inBase',inB /*invalid/illegal arg:   inBase. */
if toB<2   | tob>mxB  then call erb 'toBase',toB /*    "      "     "     toBase. */
if x==''              then call erm              /*    "      "     "     number. */
sigX=left(x, 1)                           /*obtain a possible leading sign.*/
if pos(sigX, '-+')\==0  then x=substr(x, 2)      /*X  number has a leading sign?  */
else sigX=               /*           ··· no leading sign.*/
#=0
do j=1  for length(x);  _=substr(x, j, 1)  /*convert X, base inB ──► base 10*/
v=pos(_, @@@)                              /*get the value of this "digit". */
if v==0 | v>inB  then call erd x,j,inB     /*is this an illegal "numeral" ? */
#=# * inB + v - 1                          /*construct new num, dig by dig. */
end   /*j*/
y=
do  while  # >= toB                        /*convert #, base 10 ──► base toB*/
y=substr(@@@, (# // toB) + 1, 1)y          /*construct the number for output*/
#=# % toB                                  /* ··· and whittle  #  down also.*/
end   /*while*/

y=sigX || substr(@@@, #+1, 1)y                   /*prepend the sign if it existed.*/
return y                                         /*return the number in base  toB.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
erb:  call ser  'illegal'   arg(2)   "base: "   arg(1)   "must be in range:  2──► "    mxB
erd:  call ser  'illegal "digit" in'            x":"     _
erm:  call ser  'no argument specified.'
ser:  say; say  '***error***';             say arg(1);     say;      exit 13
```
output   when using the input of:   6   2
```displaying a  6  row Floyd's triangle in base 2:

1
10    11
100   101   110
111  1000  1001  1010
1011  1100  1101  1110  1111
10000 10001 10010 10011 10100 10101
```
output   when using the input of:   23   2
```displaying a  12  row Floyd's triangle in base 2:

1
10      11
100     101     110
111    1000    1001    1010
1011    1100    1101    1110    1111
10000   10001   10010   10011   10100   10101
10110   10111   11000   11001   11010   11011   11100
11101   11110   11111  100000  100001  100010  100011  100100
100101  100110  100111  101000  101001  101010  101011  101100  101101
101110  101111  110000  110001  110010  110011  110100  110101  110110  110111
111000  111001  111010  111011  111100  111101  111110  111111 1000000 1000001 1000010
1000011 1000100 1000101 1000110 1000111 1001000 1001001 1001010 1001011 1001100 1001101 1001110
```
output   when using the input of:   40   81
```displaying a  40  row Floyd's triangle in base 81:

1
2  3
4  5  6
7  8  9  a
b  c  d  e  f
g  h  i  j  k  l
m  n  o  p  q  r  s
t  u  v  w  x  y  z  A
B  C  D  E  F  G  H  I  J
K  L  M  N  O  P  Q  R  S  T
U  V  W  X  Y  Z  <  >  [  ]  {
}  (  )  ?  ~  !  @  #  \$  %  ^  &
*  _ 10 11 12 13 14 15 16 17 18 19 1a
1b 1c 1d 1e 1f 1g 1h 1i 1j 1k 1l 1m 1n 1o
1p 1q 1r 1s 1t 1u 1v 1w 1x 1y 1z 1A 1B 1C 1D
1E 1F 1G 1H 1I 1J 1K 1L 1M 1N 1O 1P 1Q 1R 1S 1T
1U 1V 1W 1X 1Y 1Z 1< 1> 1[ 1] 1{ 1} 1( 1) 1? 1~ 1!
1@ 1# 1\$ 1% 1^ 1& 1* 1_ 20 21 22 23 24 25 26 27 28 29
2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 2m 2n 2o 2p 2q 2r 2s
2t 2u 2v 2w 2x 2y 2z 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 2M
2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X 2Y 2Z 2< 2> 2[ 2] 2{ 2} 2( 2)
2? 2~ 2! 2@ 2# 2\$ 2% 2^ 2& 2* 2_ 30 31 32 33 34 35 36 37 38 39 3a
3b 3c 3d 3e 3f 3g 3h 3i 3j 3k 3l 3m 3n 3o 3p 3q 3r 3s 3t 3u 3v 3w 3x
3y 3z 3A 3B 3C 3D 3E 3F 3G 3H 3I 3J 3K 3L 3M 3N 3O 3P 3Q 3R 3S 3T 3U 3V
3W 3X 3Y 3Z 3< 3> 3[ 3] 3{ 3} 3( 3) 3? 3~ 3! 3@ 3# 3\$ 3% 3^ 3& 3* 3_ 40 41
42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f 4g 4h 4i 4j 4k 4l 4m 4n 4o 4p 4q 4r
4s 4t 4u 4v 4w 4x 4y 4z 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 4M 4N 4O 4P 4Q 4R 4S
4T 4U 4V 4W 4X 4Y 4Z 4< 4> 4[ 4] 4{ 4} 4( 4) 4? 4~ 4! 4@ 4# 4\$ 4% 4^ 4& 4* 4_ 50 51
52 53 54 55 56 57 58 59 5a 5b 5c 5d 5e 5f 5g 5h 5i 5j 5k 5l 5m 5n 5o 5p 5q 5r 5s 5t 5u
5v 5w 5x 5y 5z 5A 5B 5C 5D 5E 5F 5G 5H 5I 5J 5K 5L 5M 5N 5O 5P 5Q 5R 5S 5T 5U 5V 5W 5X 5Y
5Z 5< 5> 5[ 5] 5{ 5} 5( 5) 5? 5~ 5! 5@ 5# 5\$ 5% 5^ 5& 5* 5_ 60 61 62 63 64 65 66 67 68 69 6a
6b 6c 6d 6e 6f 6g 6h 6i 6j 6k 6l 6m 6n 6o 6p 6q 6r 6s 6t 6u 6v 6w 6x 6y 6z 6A 6B 6C 6D 6E 6F 6G
6H 6I 6J 6K 6L 6M 6N 6O 6P 6Q 6R 6S 6T 6U 6V 6W 6X 6Y 6Z 6< 6> 6[ 6] 6{ 6} 6( 6) 6? 6~ 6! 6@ 6# 6\$
6% 6^ 6& 6* 6_ 70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e 7f 7g 7h 7i 7j 7k 7l 7m 7n 7o 7p 7q 7r 7s
7t 7u 7v 7w 7x 7y 7z 7A 7B 7C 7D 7E 7F 7G 7H 7I 7J 7K 7L 7M 7N 7O 7P 7Q 7R 7S 7T 7U 7V 7W 7X 7Y 7Z 7< 7>
7[ 7] 7{ 7} 7( 7) 7? 7~ 7! 7@ 7# 7\$ 7% 7^ 7& 7* 7_ 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f 8g 8h 8i
8j 8k 8l 8m 8n 8o 8p 8q 8r 8s 8t 8u 8v 8w 8x 8y 8z 8A 8B 8C 8D 8E 8F 8G 8H 8I 8J 8K 8L 8M 8N 8O 8P 8Q 8R 8S 8T
8U 8V 8W 8X 8Y 8Z 8< 8> 8[ 8] 8{ 8} 8( 8) 8? 8~ 8! 8@ 8# 8\$ 8% 8^ 8& 8* 8_ 90 91 92 93 94 95 96 97 98 99 9a 9b 9c
9d 9e 9f 9g 9h 9i 9j 9k 9l 9m 9n 9o 9p 9q 9r 9s 9t 9u 9v 9w 9x 9y 9z 9A 9B 9C 9D 9E 9F 9G 9H 9I 9J 9K 9L 9M 9N 9O 9P
9Q 9R 9S 9T 9U 9V 9W 9X 9Y 9Z 9< 9> 9[ 9] 9{ 9} 9( 9) 9? 9~ 9! 9@ 9# 9\$ 9% 9^ 9& 9* 9_ a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa
```

## Ring

```rows = 10
n = 0
for r = 1 to rows
for c = 1 to r
n = n + 1
see string(n) + " "
next
see nl
next```

Output:

```1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65 66
67 68 69 70 71 72 73 74 75 76 77 78
79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## RPL

HP-28 display has 4 lines only, so the task must be run on an HP-48 or greater to achieve n=5, with the advantage of benefitting from additional instructions: `INCR` increments a variable and returns its updated value and `FREEZE` acts as a `DO UNTIL KEY END` loop.

n=14 is out of reach for HP-48+, since only capable of displaying 22 characters per line.

RPL code Comment
```≪
0 → c
≪ CLLCD 1 5 FOR line
"" DO
IF c 9 < THEN " " + END
'c' INCR →STR + " " +
UNTIL line DUP 1 + * 2 / c == END
line DISP
NEXT 3 FREEZE
≫ ≫ ‘FLOYD’ STO
```
```FLOYD  ( -- )
initialize counter
clear screen, for line=1 to 5
initialize output string, loop
if counter<9 then add one space
increment counter and put it in string
until line*(line+1)/2 == counter
display string
freeze screen until key pressed
.
```

## Ruby

```def floyd(rows)
max = (rows * (rows + 1)) / 2
widths = ((max - rows + 1)..max).map {|n| n.to_s.length + 1}
n = 0
rows.times do |r|
puts (0..r).map {|i| n += 1; "%#{widths[i]}d" % n}.join
end
end

floyd(5)
floyd(14)
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Run BASIC

```input "Number of rows: "; rows
dim colSize(rows)
for col=1 to rows
colSize(col) = len(str\$(col + rows * (rows-1)/2))
next

thisNum = 1
for r = 1 to rows
for col = 1 to r
print right\$( "  "+str\$(thisNum), colSize(col)); " ";
thisNum = thisNum + 1
next
print
next```
```Number of rows: ?14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105 ```

## Rust

```fn main() {
floyds_triangle(5);
floyds_triangle(14);
}

fn floyds_triangle(n: u32) {
let mut triangle: Vec<Vec<String>> = Vec::new();
let mut current = 0;
for i in 1..=n {
let mut v = Vec::new();
for _ in 0..i {
current += 1;
v.push(current);
}
let row = v.iter().map(|x| x.to_string()).collect::<Vec<_>>();
triangle.push(row);
}

for row in &triangle {
let arranged_row: Vec<_> = row
.iter()
.enumerate()
.map(|(i, number)| {
let space_len = triangle.last().unwrap()[i].len() - number.len() + 1;
let spaces = " ".repeat(space_len);
})
.collect();
println!("{}", arranged_row.join(""))
}
}
```

## Scala

```def floydstriangle( n:Int ) = {
val s = (1 to n)
val t = s map {i => (s.take(i-1).sum) + 1}

(s zip t) foreach { n =>
var m = n._2;

for( i <- 0 until n._1 ) {
val w = (t.last + i).toString.length + 1  // Column width from last row
print("           " + m takeRight w )
m+=1
}

print("\n")
}
}

// Test
floydstriangle(5)
floydstriangle(14)
```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105

```

## Seed7

```\$ include "seed7_05.s7i";

const proc: writeFloyd (in integer: rows) is func
local
var integer: number is 1;
var integer: numBeforeLastLine is 0;
var integer: line is 0;
var integer: column is 0;
begin
numBeforeLastLine := rows * pred(rows) div 2;
for line range 1 to rows do
for column range 1 to line do
if column <> 1 then
write(" ");
end if;
incr(number);
end for;
writeln;
end for;
end func;

const proc: main is func
begin
writeFloyd(5);
writeFloyd(14);
end func;```

Output:

``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## SETL

```program floyd_triangle;
floyd(5);
print;
floyd(14);
print;

proc floyd(rows);
maxno := rows * (rows+1) div 2;
n := 1;
loop for row in [1..rows] do
loop for col in [1..row] do
nprint(lpad(str n, 1 + #str (maxno - rows + col)));
n +:=1;
end loop;
print;
end loop;
end proc;
end program;```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Sidef

```func floyd(rows, n=1) {
var max = Math.range_sum(1, rows)
var widths = (max-rows .. max-1 -> map{.+n->to_s.len})
{ |r|
say %'#{1..r -> map{|i| "%#{widths[i-1]}d" % n++}.join(" ")}'
} << 1..rows
}

floyd(5)     # or: floyd(5, 88)
floyd(14)    # or: floyd(14, 900)
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## SPL

```floyd(5)
floyd(14)

floyd(n)=
k = 0
> r, 1..n
s = ""
> j, 1..r
k += 1
f = ">"+#.upper(#.log10((n-1)*n/2+j+1)+1)+">"
s += #.str(k,f)
<
#.output(s)
<
.```
Output:
```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## Tcl

```proc floydTriangle n {
# Compute the column widths
for {set i [expr {\$n*(\$n-1)/2+1}]} {\$i <= \$n*(\$n+1)/2} {incr i} {
lappend w [string length \$i]
}
# Print the triangle
for {set i 0; set j 1} {\$j <= \$n} {incr j} {
for {set p -1; set k 0} {\$k < \$j} {incr k} {
puts -nonewline [format "%*d " [lindex \$w [incr p]] [incr i]]
}
puts ""
}
}

# Demonstration
puts "Floyd 5:"
floydTriangle 5
puts "Floyd 14:"
floydTriangle 14
```
Output:
```Floyd 5:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
Floyd 14:
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## TXR

```(defun flotri (n)
(let* ((last (trunc (* n (+ n 1)) 2))
(colw (mapcar [chain tostring length]
(range (- last n -1) last)))
(x 0))
(each ((r (range* 0 n)))
(each ((c (range 0 r)))
(format t " ~*a" [colw c] (inc x)))
(put-line))))

(defun usage (msg)
(put-line `error: @msg`)
(put-line `usage:\n@(ldiff *full-args* *args*) <smallish-positive-integer>`)
(exit 1))

(tree-case *args*
((num blah . etc) (usage "too many arguments"))
((num) (flotri (int-str num)))
(() (usage "need an argument")))```
Output:
```\$ txr floyds-triangle.tl
error: need an argument
usage:
txr floyds-triangle.tl <smallish-positive-integer>
\$ txr floyds-triangle.txr 1 2
error: too many arguments
usage:
txr floyds-triangle.tl <smallish-positive-integer>
\$ txr floyds-triangle.tl 5
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
\$ txr floyds-triangle.tl 14
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Uiua

```Floyd ← ⊜□▽.⟜(+1⇡/+)+1⇡
Print ← (
⬚""≡°⋕       # Stringify terms
/↥≡◇⧻♭.      # Get max length
≡(&p/\$"_ _") # Print
)

Print Floyd 4
&p""
Print Floyd 14```
Output:
``` 1
2 3
4 5 6
7 8 9 10

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## V (Vlang)

```fn main() {
floyd(5)
floyd(14)
}

fn floyd(rows int) {
println('Floyd \${rows}:')
mut num:=0
for row in 1..rows+2{
for _ in 1..row{
num++
fnum:='  '+num.str()
print(fnum[fnum.len-3..]+' ')
}
println('')
}
}```
Output:
```Floyd 5:

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
Floyd 14:

1
2   3
4   5   6
7   8   9  10
11  12  13  14  15
16  17  18  19  20  21
22  23  24  25  26  27  28
29  30  31  32  33  34  35  36
37  38  39  40  41  42  43  44  45
46  47  48  49  50  51  52  53  54  55
56  57  58  59  60  61  62  63  64  65  66
67  68  69  70  71  72  73  74  75  76  77  78
79  80  81  82  83  84  85  86  87  88  89  90  91
92  93  94  95  96  97  98  99 100 101 102 103 104 105
```

## VBA

Solution in Microsoft Office Word. Based on VBScript

```Option Explicit
Dim o As String
Sub floyd(L As Integer)
Dim r, c, m, n As Integer
n = L * (L - 1) / 2
m = 1
For r = 1 To L
o = o & vbCrLf
For c = 1 To r
o = o & Space(Len(CStr(n + c)) - Len(CStr(m))) & m & " "
m = m + 1
Next
Next
End Sub
Sub triangle()
o = "5 lines"
Call floyd(5)
o = o & vbCrLf & "14 lines"
Call floyd(14)
With Selection
.Font.Name = "Courier New"
.TypeText Text:=o
End With
End Sub```
Output:
```5 lines
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

14 lines
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## VBScript

Works with: Windows Script Host version *
```' Read the number of rows to use..

' Get the first number of the final row so we can calculate widths...
intLastRowStart = (intRows ^ 2 - intRows) \ 2 + 1

For i = 1 To intRows
intLastRow = intLastRowStart
For j = 1 To i
k = k + 1
WScript.StdOut.Write Space(Len(intLastRow) - Len(k)) & k & " "
intLastRow = intLastRow + 1
Next
WScript.StdOut.WriteLine ""
Next
```

## Visual Basic .NET

Translation of: C#
```Imports System.Text

Module Module1

Function MakeTriangle(rows As Integer) As String
Dim maxValue As Integer = (rows * (rows + 1)) / 2
Dim digit = 0
Dim output As New StringBuilder

For row = 1 To rows
For column = 0 To row - 1
Dim colMaxDigit = (maxValue - rows) + column + 1
If column > 0 Then
output.Append(" ")
End If

digit = digit + 1
Next

output.AppendLine()
Next

Return output.ToString()
End Function

Sub Main()
Dim args = Environment.GetCommandLineArgs()
Dim count As Integer

If args.Length > 1 AndAlso Integer.TryParse(args(1), count) AndAlso count > 0 Then
Console.WriteLine(MakeTriangle(count))
Else
Console.WriteLine(MakeTriangle(5))
Console.WriteLine()
Console.WriteLine(MakeTriangle(14))
End If
End Sub

End Module
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105```

## Wren

Library: Wren-fmt
```import "./fmt" for Fmt

var floyd = Fn.new { |n|
var k = 1
for (i in 1..n) {
for (j in 1..i) {
Fmt.write("\$*d ", (j < 9) ? 2 : 3, k)
k = k + 1
}
System.print()
}
}

System.print("Floyd(5):")
floyd.call(5)
System.print("\nFloyd(14):")
floyd.call(14)
```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

Floyd(14):
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## XPL0

```include c:\cxpl\codes;  \include 'code' declarations

func IntLen(N);         \Return number of digits in a positive integer
int     N;
int     I;
for I:= 1 to 20 do
[N:= N/10;  if N=0 then return I];

proc Floyd(N);          \Display Floyd's triangle
int N;
int M, Row, Col;
real F;
[M:= (N-1+1)*(N-1)/2;   \last Floyd number on second to last row
F:= 1.0;                \Floyd number counter
for Row:= 1 to N do
[for Col:= 1 to Row do
[Format(IntLen(M+Col)+1, 0);  RlOut(0, F);  F:= F+1.0];
CrLf(0);
];
]; \Floyd

[Floyd(5);
Floyd(14);
]```

Output:

```  1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## zkl

Format last line and then fit each line to that format (which is wider than terminal width before formating breaks down (at 10 digit numbers)):

```fcn lcNum(row){(row*(row+1)/2+1)}   // lazy caterer's sequence
fcn floydsTriangle(rows){
fmt:=[lcNum(rows-1)..lcNum(rows)-1].pump(String,fcn(n){
String("%",n.toString().len(),"d ")}); // eg "%2d %2d %3d %3d"
foreach row in (rows){
ns:=[lcNum(row)..lcNum(row+1)-1].walk(); // eg L(4.5,6)
fmt[0,ns.len()*4].fmt(ns.xplode()).println(); // eg "%2d %2d %2d ".fmt(4,5,6)
}
}
floydsTriangle(5); println();
floydsTriangle(14);```
Output:
``` 1
2  3
4  5  6
7  8  9 10
11 12 13 14 15

1
2  3
4  5  6
7  8  9 10
11 12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44  45
46 47 48 49 50 51 52 53  54  55
56 57 58 59 60 61 62 63  64  65  66
67 68 69 70 71 72 73 74  75  76  77  78
79 80 81 82 83 84 85 86  87  88  89  90  91
92 93 94 95 96 97 98 99 100 101 102 103 104 105
```

## ZX Spectrum Basic

```10 LET n=10: LET j=1: LET col=1
20 FOR r=1 TO n
30 FOR j=j TO j+r-1
40 PRINT TAB (col);j;
50 LET col=col+3
60 NEXT j
70 PRINT
80 LET col=1
90 NEXT r```