Fibonacci n-step number sequences: Difference between revisions
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decanacci: 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172 …
Lucas: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364 …"</syntaxhighlight>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">naccis: #[
lucas: [2 1]
fibonacci: [1 1]
tribonacci: [1 1 2]
tetranacci: [1 1 2 4]
pentanacci: [1 1 2 4 8]
hexanacci: [1 1 2 4 8 16]
heptanacci: [1 1 2 4 8 16 32]
octonacci: [1 1 2 4 8 16 32 64]
nonanacci: [1 1 2 4 8 16 32 64 128]
decanacci: [1 1 2 4 8 16 32 64 128 256]
]
anyNacci: function [start, count][
n: size start
result: new start
do.times: count-n ->
result: result ++ sum last.n:n result
return join.with:", " to [:string] result
]
loop naccis [k,v][
print [pad (k ++ ":") 12 anyNacci v 15]
]</syntaxhighlight>
{{out}}
<pre> lucas: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843
fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
tribonacci: 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136
tetranacci: 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490, 2872, 5536
pentanacci: 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930
hexanacci: 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976, 1936, 3840, 7617
heptanacci: 1, 1, 2, 4, 8, 16, 32, 64, 127, 253, 504, 1004, 2000, 3984, 7936
octonacci: 1, 1, 2, 4, 8, 16, 32, 64, 128, 255, 509, 1016, 2028, 4048, 8080
nonanacci: 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2040, 4076, 8144
decanacci: 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172</pre>
=={{header|AutoHotkey}}==
Line 838 ⟶ 878:
</pre>
=={{header|
==={{header|BASIC256}}===
<syntaxhighlight lang="basic256"># Rosetta Code problem: https://www.rosettacode.org/wiki/Fibonacci_n-step_number_sequences
# by Jjuanhdez, 06/2022
Line 901 ⟶ 942:
decanacci => 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, ...
lucas => 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, ...</pre>
==={{header|Chipmunk Basic}}===
{{trans|BASIC256}}
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="vbnet">100 sub fib(a())
110 erase f
120 dim f(24)
130 b = 0
140 for x = 1 to ubound(a)
150 b = b+1
160 f(x) = a(x)
170 next x
180 for i = b to 12+b
190 print using "#### ";f(i-b+1);
200 for j = (i-b+1) to i
210 f(i+1) = f(i+1)+f(j)
220 next j
230 next i
240 print
250 end sub
260 cls
270 print " fibonacci =>";
280 dim a(2)
290 a(1) = 1 : a(2) = 1
300 fib(a())
310 print " tribonacci =>";
320 dim a(3)
330 a(1) = 1 : a(2) = 1 : a(3) = 2
340 fib(a())
350 print " tetranacci =>";
360 dim c(4)
370 c(1) = 1 : c(2) = 1 : c(3) = 2 : c(4) = 4
380 fib(c())
390 print " lucas =>";
400 dim d(2)
410 d(1) = 2 : d(2) = 1
420 fib(d())
430 end</syntaxhighlight>
==={{header|QBasic}}===
{{trans|BASIC256}}
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
{{works with|QB64}}
<syntaxhighlight lang="qbasic">DECLARE SUB fib (a() AS INTEGER)
CLS
PRINT " fibonacci =>";
DIM a(1 TO 2) AS INTEGER
a(1) = 1: a(2) = 1
CALL fib(a())
PRINT " tribonacci =>";
DIM b(1 TO 3) AS INTEGER
b(1) = 1: b(2) = 1: b(3) = 2
CALL fib(b())
PRINT " tetranacci =>";
DIM c(1 TO 4) AS INTEGER
c(1) = 1: c(2) = 1: c(3) = 2: c(4) = 4
CALL fib(c())
PRINT " lucas =>";
DIM d(1 TO 2) AS INTEGER
d(1) = 2: d(2) = 1
CALL fib(d())
END
SUB fib (a() AS INTEGER)
DIM f(24)
b = 0
FOR x = 1 TO UBOUND(a)
b = b + 1
f(x) = a(x)
NEXT x
FOR i = b TO 12 + b
PRINT USING "#### "; f(i - b + 1);
FOR j = (i - b + 1) TO i
f(i + 1) = f(i + 1) + f(j)
NEXT j
NEXT i
END SUB</syntaxhighlight>
==={{header|QB64}}===
{{trans|BASIC256}}
<syntaxhighlight lang="qbasic">Rem $Dynamic
Cls
Print " fibonacci =>";
Dim a(1 To 2) As Integer
a(1) = 1
a(2) = 1
Call fib(a())
Print " tribonacci =>";
ReDim _Preserve a(1 To 3)
a(3) = 2
Call fib(a())
Print " tetranacci =>";
ReDim _Preserve a(1 To 4)
a(4) = 4
Call fib(a())
Print " lucas =>";
ReDim a(1 To 2)
a(1) = 2
a(2) = 1
Call fib(a())
End
Sub fib (a() As Integer)
Dim f(24)
b = 0
For x = 1 To UBound(a)
b = b + 1
f(x) = a(x)
Next x
For i = b To 12 + b
Print Using "#### "; f(i - b + 1);
For j = (i - b + 1) To i
f(i + 1) = f(i + 1) + f(j)
Next j
Next i
End Sub</syntaxhighlight>
=={{header|Batch File}}==
Line 1,649 ⟶ 1,809:
=={{header|Delphi}}==
See [[#Pascal]].
=={{header|EasyLang}}==
<syntaxhighlight>
proc sequ n$ val[] n . .
write n$ & ": "
il = len val[]
len val[] n
for i = il + 1 to n
for j = 1 to il
val[i] += val[i - j]
.
.
for v in val[]
write v & " "
.
print ""
.
sequ "Fibonacci" [ 1 1 ] 10
sequ "Tribonacci" [ 1 1 2 ] 10
sequ "Tetrabonacci" [ 1 1 2 4 ] 10
sequ "Lucas" [ 2 1 ] 10
</syntaxhighlight>
{{out}}
<pre>
Fibonacci: 1 1 2 3 5 8 13 21 34 55
Tribonacci: 1 1 2 4 7 13 24 44 81 149
Tetrabonacci: 1 1 2 4 8 15 29 56 108 208
Lucas: 2 1 3 4 7 11 18 29 47 76
</pre>
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">
Line 2,126 ⟶ 2,315:
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Fibonacci_n-step_number_sequences}}
'''Solution'''
According to the requirements, the program must generate a series, and the order (Fibonacci, Tribonacci, etc) should be determined according with the initial values.
In this case, the number n indicates how many terms of the series will be generated.
[[File:Fōrmulæ - Fibonacci n-step number sequences 01.png]]
The following generates a Fibonacci series of 15 terms:
[[File:Fōrmulæ - Fibonacci n-step number sequences 02.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 03.png]]
The following generates a Lucas series of 15 terms:
[[File:Fōrmulæ - Fibonacci n-step number sequences 04.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 05.png]]
The following generates a Tribonacci series of 15 terms:
[[File:Fōrmulæ - Fibonacci n-step number sequences 06.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 07.png]]
'''Generating initial values.''' The initial values can be generated by the following function:
[[File:Fōrmulæ - Fibonacci n-step number sequences 08.png]]
Note that it is a recursive function, and it calls the previously defined function. It requires the initial values as a seed: (1, 1) for Fibonacci style (Fibonacci, Tribonacci, etc), and (2, 1) for Lucas style.
The following generates the initial values for Fibonacci series.
[[File:Fōrmulæ - Fibonacci n-step number sequences 09.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 10.png]]
The following generates the initial values for Lucas series.
[[File:Fōrmulæ - Fibonacci n-step number sequences 11.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 12.png]]
'''Generating tables of series for Fibonacci and Lucas'''
This generates a tables of series for Fibonacci (15 terms), for orders 2 to 10 (Fibonacci, Tribonacci, etc.)
[[File:Fōrmulæ - Fibonacci n-step number sequences 13.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 14.png]]
This generates a tables of series for Lucas (15 terms), for orders 2 to 15:
[[File:Fōrmulæ - Fibonacci n-step number sequences 15.png]]
[[File:Fōrmulæ - Fibonacci n-step number sequences 16.png]]
=={{header|Go}}==
Line 2,230 ⟶ 2,473:
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import
import
fiblike :: [Integer] -> [Integer]
fiblike st = xs
where
xs = st <> map (sum . take n) (tails xs)
n = length st
nstep :: Int -> [Integer]
nstep n = fiblike $ take n $ 1 : iterate (2 *) 1
main :: IO ()
main = do
mapM_ (print
zipWithM_
putStr (name <> "nacci -> ")
print $ take 15 $ nstep n
)
[2 ..]
(words "fibo tribo tetra penta hexa hepta octo nona deca")</syntaxhighlight>
{{out}}
<pre>
Line 3,315 ⟶ 3,562:
writeln;
END.</syntaxhighlight>
=={{header|PascalABC.NET}}==
===Unfold===
I first define a high order function to generate infinite sequences given a lambda and a seed.
<syntaxhighlight lang="pascal">
// unfold infinite sequences. Nigel Galloway: September 8th., 2022
function unfold<gN,gG>(n:Func<gG,(gN,gG)>; g:gG): sequence of gN;
begin
var (x,r):=n(g);
yield x;
yield sequence unfold(n,r);
end;
function unfold<gN,gG>(n:Func<array of gG,(gN,array of gG)>;params g:array of gG): sequence of gN := unfold(n,g);
</syntaxhighlight>
===The Task===
Like the Pascal above but not iffy, not loopy, and not as long!
<syntaxhighlight lang="pascal">
// Fibonacci n-step number sequences. Nigel Galloway: September 8th., 2022
var nFib:=function(n:array of biginteger): (biginteger,array of biginteger)->(n.First,n[1:].Append(n.Sum).ToArray);
begin
var fib:=unfold(nFib,1bi,1bi);
fib.Take(20).Println;
var tri:=unfold(nFib,fib.Take(3));
tri.Take(20).Println;
var tet:=unfold(nFib,tri.Take(4));
tet.Take(20).Println;
var pen:=unfold(nFib,tet.Take(5));
pen.Take(20).Println;
var hex:=unfold(nFib,pen.Take(6));
hex.Take(20).Println;
var hep:=unfold(nFib,hex.Take(7));
hep.Take(20).Println;
var oct:=unfold(nFib,hep.Take(8));
oct.Take(20).Println;
var non:=unfold(nFib,oct.Take(9));
non.Take(20).Println;
var dec:=unfold(nFib,non.Take(10));
dec.Take(20).Println;
var luc:=unfold(nFib,2bi,1bi);
luc.Take(20).Println;
end.
</syntaxhighlight>
{{out}}
<pre>
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 5768 10609 19513 35890 66012
1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 10671 20569 39648 76424 147312
1 1 2 4 8 16 31 61 120 236 464 912 1793 3525 6930 13624 26784 52656 103519 203513
1 1 2 4 8 16 32 63 125 248 492 976 1936 3840 7617 15109 29970 59448 117920 233904
1 1 2 4 8 16 32 64 127 253 504 1004 2000 3984 7936 15808 31489 62725 124946 248888
1 1 2 4 8 16 32 64 128 255 509 1016 2028 4048 8080 16128 32192 64256 128257 256005
1 1 2 4 8 16 32 64 128 256 511 1021 2040 4076 8144 16272 32512 64960 129792 259328
1 1 2 4 8 16 32 64 128 256 512 1023 2045 4088 8172 16336 32656 65280 130496 260864
2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349
</pre>
=={{header|Perl}}==
Line 4,169 ⟶ 4,472:
Lucas:
2 1 3 4 7 11 18 29 47 76 123 199 ...
</pre>
=={{header|RPL}}==
≪ OVER SIZE → len n
≪ LIST→
<span style="color:red">1</span> + len '''FOR''' j
n DUPN
<span style="color:red">2</span> n '''START''' + '''NEXT'''
'''NEXT''' len →LIST
≫ ≫ ‘<span style="color:blue">NFIB</span>’ STO
<span style="color:red">{1 1} 15</span> <span style="color:blue">NFIB</span>
DUP <span style="color:red">1 3</span> SUB <span style="color:red">15</span> <span style="color:blue">NFIB</span>
DUP <span style="color:red">1 4</span> SUB <span style="color:red">15</span> <span style="color:blue">NFIB</span>
<span style="color:red">{2 1} 15</span> <span style="color:blue">NFIB</span>
{{out}}
<pre>
4: { 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 }
3: { 1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 }
2: { 1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 }
1: { 2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 }
</pre>
Line 4,439 ⟶ 4,763:
var len = xs.len
len >= k && break
xs << xs.
}
return xs
Line 4,760 ⟶ 5,084:
</pre>
=={{header|V (Vlang)}}==
{{trans|Wren}}
<syntaxhighlight lang="v (vlang)">fn fib_n(initial []int, num_terms int) []int {
n := initial.len
if n < 2 || num_terms < 0 {panic("Invalid argument(s).")}
Line 4,815 ⟶ 5,139:
{{trans|Kotlin}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
var fibN = Fn.new { |initial, numTerms|
| |||