# Leonardo numbers

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Leonardo numbers
You are encouraged to solve this task according to the task description, using any language you may know.

Leonardo numbers   are also known as the   Leonardo series.

The   Leonardo numbers   are a sequence of numbers defined by:

```       L(0) = 1                                          [1st equation]
L(1) = 1                                          [2nd equation]
L(n) = L(n-1)  +    L(n-2)   +  1                 [3rd equation]
─── also ───
L(n) =      2  *  Fib(n+1)   -  1                 [4th equation]
```
where the   + 1   will herein be known as the   add   number.
where the   FIB   is the   Fibonacci numbers.

This task will be using the 3rd equation (above) to calculate the Leonardo numbers.

Edsger W. Dijkstra   used   Leonardo numbers   as an integral part of his   smoothsort   algorithm.

The first few Leonardo numbers are:

```    1   1   3   5   9   15   25   41   67   109   177   287   465   753   1219   1973   3193   5167   8361  ···
```

•   show the 1st   25   Leonardo numbers, starting at L(0).
•   allow the first two Leonardo numbers to be specified   [for L(0) and L(1)].
•   allow the   add   number to be specified   (1 is the default).
•   show the 1st   25   Leonardo numbers, specifying 0 and 1 for L(0) and L(1), and 0 for the add number.

(The last task requirement will produce the Fibonacci numbers.)

## 11l

Translation of: C++
```F leo_numbers(cnt, =l0 = 1, =l1 = 1, add = 1)
L 1..cnt
print(l0, end' ‘ ’)
(l0, l1) = (l1, l0 + l1 + add)
print()

print(‘Leonardo Numbers: ’, end' ‘’)
leo_numbers(25)
print(‘Fibonacci Numbers: ’, end' ‘’)
leo_numbers(25, 0, 1, 0)```
Output:
```Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Action!

```CARD FUNC Leonardo(BYTE n)
CARD curr,prev,tmp

IF n<=1 THEN
RETURN (1)
FI

prev=1
curr=1
DO
tmp=prev
prev=curr
curr==+tmp+1
n==-1
UNTIL n=1
OD
RETURN (curr)

PROC Main()
BYTE n
CARD l

Put(125) ;clear screen

FOR n=0 TO 22 ;limited to 22 because of CARD limitations
DO
l=Leonardo(n)
IF n MOD 2=0 THEN
Position(2,n/2+1)
ELSE
Position(21,n/2+1)
FI
PrintF("L(%B)=%U",n,l)
OD
RETURN```
Output:
```L(0)=1             L(1)=1
L(2)=3             L(3)=5
L(4)=9             L(5)=15
L(6)=25            L(7)=41
L(8)=67            L(9)=109
L(10)=177          L(11)=287
L(12)=465          L(13)=753
L(14)=1219         L(15)=1973
L(16)=3193         L(17)=5167
L(18)=8361         L(19)=13529
L(20)=21891        L(21)=35421
L(22)=57313
```

```with Ada.Text_IO; use Ada.Text_IO;

procedure Leonardo is

function Leo
(N      : Natural;
Step   : Natural := 1;
First  : Natural := 1;
Second : Natural := 1) return Natural   is
L : array (0..1) of Natural := (First, Second);
begin
for i in 1 .. N loop
L := (L(1), L(0)+L(1)+Step);
end loop;
return L (0);
end Leo;

begin
Put_Line ("First 25 Leonardo numbers:");
for I in 0 .. 24 loop
Put (Integer'Image (Leo (I)));
end loop;
New_Line;
Put_Line ("First 25 Leonardo numbers with L(0) = 0, L(1) = 1, " &
"step = 0 (fibonacci numbers):");
for I in 0 .. 24 loop
Put (Integer'Image (Leo (I, 0, 0, 1)));
end loop;
New_Line;
end Leonardo;
```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## ALGOL 68

```BEGIN
# leonardo number parameters #
MODE LEONARDO = STRUCT( INT l0, l1, add number );
# default leonardo number parameters #
LEONARDO leonardo numbers = LEONARDO( 1, 1, 1 );
# operators to allow us to specify non-default parameters #
PRIO WITHLZERO = 9, WITHLONE = 9, WITHADDNUMBER = 9;
OP   WITHLZERO     = ( LEONARDO parameters, INT l0         )LEONARDO:
LEONARDO( l0, l1 OF parameters, add number OF parameters );
OP   WITHLONE      = ( LEONARDO parameters, INT l1         )LEONARDO:
LEONARDO( l0 OF parameters, l1, add number OF parameters );
LEONARDO( l0 OF parameters, l1 OF parameters, add number );
# show the first n Leonardo numbers with the specified parameters #
PROC show = ( INT n, LEONARDO parameters )VOID:
IF n > 0 THEN
INT l0         = l0         OF parameters;
INT l1         = l1         OF parameters;
print( ( whole( l0, 0 ), " " ) );
IF n > 1 THEN
print( ( whole( l1, 0 ), " " ) );
INT lp := l0;
INT ln := l1;
FROM 2 TO n - 1 DO
INT next = ln + lp + add number;
lp := ln;
ln := next;
print( ( whole( ln, 0 ), " " ) )
OD
FI
FI # show # ;

# first series #
print( ( "First 25 Leonardo numbers", newline ) );
show( 25, leonardo numbers );
print( ( newline ) );
# second series #
print( ( "First 25 Leonardo numbers from 0, 1 with add number = 0", newline ) );
show( 25, leonardo numbers WITHLZERO 0 WITHADDNUMBER 0 );
print( ( newline ) )
END```
Output:
```First 25 Leonardo numbers
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers from 0, 1 with add number = 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## AppleScript

### Functional

Translation of: Python
(Generator version)

Drawing N items from a non-finite generator:

```------------------------ GENERATOR -------------------------

-- leo :: Int -> Int -> Int -> Generator [Int]
on leo(L0, L1, delta)
script
property x : L0
property y : L1
on |λ|()
set n to x
set {x, y} to {y, x + y + delta}
return n
end |λ|
end script
end leo

--------------------------- TEST ---------------------------
on run
set leonardo to leo(1, 1, 1)
set fibonacci to leo(0, 1, 0)

unlines({"First 25 Leonardo numbers:", ¬
twoLines(take(25, leonardo)), "", ¬
"First 25 Fibonacci numbers:", ¬
twoLines(take(25, fibonacci))})
end run

------------------------ FORMATTING ------------------------

-- twoLines :: [Int] -> String
on twoLines(xs)
script row
on |λ|(ns)
tab & intercalate(", ", ns)
end |λ|
end script
return unlines(map(row, chunksOf(16, xs)))
end twoLines

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

-- chunksOf :: Int -> [a] -> [[a]]
on chunksOf(n, xs)
set lng to length of xs
script go
on |λ|(a, i)
set x to (i + n) - 1
if x ≥ lng then
a & {items i thru -1 of xs}
else
a & {items i thru x of xs}
end if
end |λ|
end script
foldl(go, {}, enumFromThenTo(1, n, lng))
end chunksOf

-- enumFromThenTo :: Int -> Int -> Int -> [Int]
on enumFromThenTo(x1, x2, y)
set xs to {}
set d to max(1, (x2 - x1))
repeat with i from x1 to y by d
set end of xs to i
end repeat
return xs
end enumFromThenTo

-- 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

-- intercalate :: String -> [String] -> String
on intercalate(sep, xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, sep}
set s to xs as text
set my text item delimiters to dlm
return s
end intercalate

-- 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

-- 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

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

-- 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:
```First 25 Leonardo numbers:
1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973
1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049

First 25 Fibonacci numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368```

### Idiomatic

Allowing optional 'L0', 'L1', and/or 'add' specs with any version of AppleScript.

```-- spec: record containing none, some, or all of the 'L0', 'L1', and 'add' values.
on leonardos(spec, quantity)
-- Assign the spec values to variables, using defaults for any not given.
-- Build the output list.
script o
property output : {a, b}
end script
repeat (quantity - 2) times
set c to a + b + inc
set end of o's output to c
set a to b
set b to c
end repeat

return o's output
end leonardos

local output, astid
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to ", "
set output to "1st 25 Leonardos:
" & leonardos({}, 25) & "
1st 25 Fibonaccis:
" & leonardos({L0:0, L1:1, add:0}, 25)
set AppleScript's text item delimiters to astid
return output
```
Output:
```"1st 25 Leonardos:
1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049
1st 25 Fibonaccis:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368"
```

## Arturo

```L: function [n l0 l1 ladd].memoize[
(n=0)? -> l0 [
(n=1)? -> l1
]
]

Leonardo: function [z]-> L z 1 1 1

print "The first 25 Leonardo numbers:"
print map 0..24 => Leonardo
print ""
print "The first 25 Leonardo numbers with L0=0, L1=1, LADD=0"
print map 0..24 'x -> L x 0 1 0
```
Output:
```The first 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Leonardo numbers with L0=0, L1=1, LADD=0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368```

## AutoHotkey

```Leonardo(n, L0:=1, L1:=1, step:=1){
if n=0
return L0
if n=1
return L1
return Leonardo(n-1, L0, L1, step) + Leonardo(n-2, L0, L1, step) + step
}
```
Examples:
```output := "1st 25 Leonardo numbers, starting at L(0).`n"
loop, 25
output .= Leonardo(A_Index-1) " "
output .= "`n`n1st 25 Leonardo numbers, specifying 0 and 1 for L(0) and L(1), and 0 for the add number:`n"
loop, 25
output .= Leonardo(A_Index-1, 0, 1, 0) " "
MsgBox % output
return
```
Output:
```1st 25 Leonardo numbers, starting at L(0).
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

1st 25 Leonardo numbers, specifying 0 and 1 for L(0) and L(1), and 0 for the add number:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368```

## AWK

```# syntax: GAWK -f LEONARDO_NUMBERS.AWK
BEGIN {
leonardo(1,1,1,"Leonardo")
leonardo(0,1,0,"Fibonacci")
exit(0)
}
function leonardo(L0,L1,step,text,  i,tmp) {
printf("%s numbers (%d,%d,%d):\n",text,L0,L1,step)
for (i=1; i<=25; i++) {
if (i == 1) {
printf("%d ",L0)
}
else if (i == 2) {
printf("%d ",L1)
}
else {
printf("%d ",L0+L1+step)
tmp = L0
L0 = L1
L1 = tmp + L1 + step
}
}
printf("\n")
}
```
Output:
```Leonardo numbers (1,1,1):
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci numbers (0,1,0):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Bash

```#!/bin/bash

function leonardo_number () {
L0_value=\${2:-1}
L1_value=\${3:-1}
leonardo_numbers=(\$L0_value \$L1_value)
for (( i = 2; i < \$1; ++i))
do
leonardo_numbers+=( \$((leonardo_numbers[i-1] + leonardo_numbers[i-2] + Add)) )
done
echo "\${leonardo_numbers[*]}"
}
```
Output:
```leonardo_number 25
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

leonardo_number 25 0 1 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## BASIC

### BASIC256

```subroutine leonardo(L0, L1, suma, texto)
print "Numeros de " + texto + " (" + L0 + "," + L1 + "," + suma + "):"
for i = 1 to 25
if i = 1 then
print L0 + " ";
else
if i = 2 then
print L1 + " ";
else
print L0 + L1 + suma + " ";
tmp = L0
L0 = L1
L1 = tmp + L1 + suma
end if
end if
next i
print chr(10)
end subroutine

#--- Programa Principal ---
call leonardo(1,1,1,"Leonardo")
call leonardo(0,1,0,"Fibonacci")
end```
Output:
```Numeros de Leonardo (1,1,1):
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Numeros de Fibonacci (0,1,0):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

### IS-BASIC

```100 PROGRAM "Leonardo.bas"
110 INPUT PROMPT "Enter values of L0, L1, and ADD, separated by comas: ":L0,L1,ADD
120 PRINT L0;L1;
130 FOR I=3 TO 25
160   PRINT L1;
170 NEXT
180 PRINT```

### Sinclair ZX81 BASIC

Runs on the 1k RAM model with room to spare; hence the long(ish) variable names. The parameters are read from the keyboard.

``` 10 INPUT L0
20 INPUT L1
40 PRINT L0;" ";L1;
50 FOR I=3 TO 25
60 LET TEMP=L1
80 LET L0=TEMP
90 PRINT " ";L1;
100 NEXT I
```
Input:
```1
1
1```
Output:
`1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049`
Input:
```0
1
0```
Output:
` 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368`

## BBC BASIC

It's a shame when fonts don't make much of a distinction between l lower-case L and 1 the number One.

```REM >leonardo
:
PRINT "Enter values of L0, L1, and ADD, separated by commas:"
PRINT l0% ' l1%
FOR i% = 3 TO 25
temp% = l1%
l0% = temp%
PRINT l1%
NEXT
PRINT
END
```
Output:
```Enter values of L0, L1, and ADD, separated by commas:
?1, 1, 1
1
1
3
5
9
15
25
41
67
109
177
287
465
753
1219
1973
3193
5167
8361
13529
21891
35421
57313
92735
150049```
```Enter values of L0, L1, and ADD, separated by commas:
?0, 1, 0
0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368```

## Burlesque

```blsq ) 1 1 1{.+\/.+}\/+]23!CCLm]wdsh
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

blsq ) 0 1 0{.+\/.+}\/+]23!CCLm]wdsh
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368```

## C

This implementation fulfills the task requirements which state that the first 2 terms and the step increment should be specified. Many other implementations on this page only print out the first 25 numbers.

```#include<stdio.h>

void leonardo(int a,int b,int step,int num){

int i,temp;

printf("First 25 Leonardo numbers : \n");

for(i=1;i<=num;i++){
if(i==1)
printf(" %d",a);
else if(i==2)
printf(" %d",b);
else{
printf(" %d",a+b+step);
temp = a;
a = b;
b = temp+b+step;
}
}
}

int main()
{
int a,b,step;

printf("Enter first two Leonardo numbers and increment step : ");

scanf("%d%d%d",&a,&b,&step);

leonardo(a,b,step,25);

return 0;
}
```

Output : Normal Leonardo Series :

```Enter first two Leonardo numbers and increment step : 1 1 1
First 25 Leonardo numbers :
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
```

Fibonacci Series :

```Enter first two Leonardo numbers and increment step : 0 1 0
First 25 Leonardo numbers :
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## C#

Works with: C sharp version 7
```using System;
using System.Linq;

public class Program
{
public static void Main() {
Console.WriteLine(string.Join(" ", Leonardo().Take(25)));
Console.WriteLine(string.Join(" ", Leonardo(L0: 0, L1: 1, add: 0).Take(25)));
}

public static IEnumerable<int> Leonardo(int L0 = 1, int L1 = 1, int add = 1) {
while (true) {
yield return L0;
(L0, L1) = (L1, L0 + L1 + add);
}
}
}
```
Output:
```1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## C++

```#include <iostream>

void leoN( int cnt, int l0 = 1, int l1 = 1, int add = 1 ) {
int t;
for( int i = 0; i < cnt; i++ ) {
std::cout << l0 << " ";
t = l0 + l1 + add; l0 = l1; l1 = t;
}
}
int main( int argc, char* argv[] ) {
std::cout << "Leonardo Numbers: "; leoN( 25 );
std::cout << "\n\nFibonacci Numbers: "; leoN( 25, 0, 1, 0 );
return 0;
}
```
Output:
```
Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

```

## Common Lisp

```;;;
;;; leo - calculates the first n number from a leo sequence.
;;; The first argument n is the number of values to return. The next three arguments a, b, add are optional.
;;; Default values provide the "original" leonardo numbers as defined in the task.
;;; a and b are the first and second element of the leonardo sequence.
;;;

(defun leo (n &optional (a 1) (b 1) (add 1))
(labels ((iterate (n foo)
(if (zerop n) (reverse foo)
(iterate (- n 1)
(cons (+ (first foo) (second foo) add) foo)))))
(cond ((= n 1) (list a))
(T       (iterate (- n 2) (list b a))))))
```
Output:
```> (leo 25)
(1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049)
> (leo 25 0 1 0)
(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368)
```

## Crystal

Translation of: Python
```def leonardo(l_zero, l_one, add, amount)
terms = [l_zero, l_one]
while terms.size < amount
new = terms[-1] + terms[-2]
terms << new
end
terms
end

puts "First 25 Leonardo numbers: \n#{ leonardo(1,1,1,25) }"
puts "Leonardo numbers with fibonacci parameters:\n#{ leonardo(0,1,0,25) }"
```
Output:
```First 25 Leonardo numbers:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
Leonardo numbers with fibonacci parameters:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]
```

## D

Translation of: C++
```import std.stdio;

void main() {
write("Leonardo Numbers: ");
leonardoNumbers( 25 );

write("Fibonacci Numbers: ");
leonardoNumbers( 25, 0, 1, 0 );
}

void leonardoNumbers(int count, int l0=1, int l1=1, int add=1) {
int t;
for (int i=0; i<count; ++i) {
write(l0, " ");
t = l0 + l1 + add;
l0 = l1;
l1 = t;
}
writeln();
}
```
Output:
```
Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

```

## F#

```open System

let leo l0 l1 d =
Seq.unfold (fun (x, y) -> Some (x, (y, x + y + d))) (l0, l1)

let leonardo = leo 1 1 1
let fibonacci = leo 0 1 0

[<EntryPoint>]
let main _ =
let leoNums = Seq.take 25 leonardo |> Seq.chunkBySize 16
printfn "First 25 of the (1, 1, 1) Leonardo numbers:\n%A" leoNums
Console.WriteLine()

let fibNums = Seq.take 25 fibonacci |> Seq.chunkBySize 16
printfn "First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci number):\n%A" fibNums

0 // return an integer exit code
```
Output:
```First 25 of the (1, 1, 1) Leonardo numbers:
seq
[[|1; 1; 3; 5; 9; 15; 25; 41; 67; 109; 177; 287; 465; 753; 1219; 1973|];
[|3193; 5167; 8361; 13529; 21891; 35421; 57313; 92735; 150049|]]

First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci number):
seq
[[|0; 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610|];
[|987; 1597; 2584; 4181; 6765; 10946; 17711; 28657; 46368|]]```

## Factor

```USING: fry io kernel math prettyprint sequences ;
IN: rosetta-code.leonardo-numbers

: first25-leonardo ( vector add -- seq )
23 swap '[ dup 2 tail* sum _ + over push ] times ;

: print-leo ( seq -- ) [ pprint bl ] each nl ;

"First 25 Leonardo numbers:" print
V{ 1 1 } 1 first25-leonardo print-leo

"First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:" print
V{ 0 1 } 0 first25-leonardo print-leo
```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Fermat

```Func Leonardo(size, l0, l1, add) =
Array leo[1,size];             {set up as a row rather than column vector; looks nicer to print}
leo[1,1]:=l0; leo[1,2]:=l1;    {fermat arrays are 1-indexed}
for i=3 to size do
od;
.;

Leonardo(25, 1, 1, 1);
[leo];

Leonardo(25, 0, 1, 0);
[leo];```
Output:
```[[  1,  1,  3,  5,  9,  15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049  ]]

[[[  1,  1,  3,  5,  9,  15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049  ]]
```

## Fortran

Happily, no monster values result for the trial run, so ordinary 32-bit integers suffice. The source style uses the F90 facilities only to name the subroutine being ended (i.e. `END SUBROUTINE LEONARDO` rather than just `END`) and the I0 format code that shows an integer without a fixed space allowance, convenient in produced well-formed messages. The "\$" format code signifies that the end of output from its WRITE statement should not trigger the starting of a new line for the next WRITE statement, convenient when rolling a sequence of values to a line of output one-by-one as they are concocted. Otherwise, the values would have to be accumulated in a suitable array and then written in one go.

Many versions of Fortran have enabled parameters to be optionally supplied and F90 has standardised a protocol, also introducing a declaration syntax that can specify multiple attributes in one statement which in this case would be `INTEGER, OPTIONAL:: AF` rather than two statements concerning AF. However, in a test run with `CALL LEONARDO(25,1,1)` the Compaq F90/95 compiler rejected this attempt because there was another invocation with four parameters, not three, in the same program unit. By adding the rigmarole for declaring a MODULE containing the subroutine LEONARDO, its worries would be assuaged. Many compilers (and linkers, for separately-compiled routines) would check neither the number nor the type of parameters so no such complaint would be made - but when run, the code might produce wrong results or crash.

The method relies on producing a sequence of values, rather than calculating L(n) from the start each time a value from the sequence is required.
```      SUBROUTINE LEONARDO(LAST,L0,L1,AF)	!Show the first LAST values of the sequence.
INTEGER LAST	!Limit to show.
INTEGER L0,L1	!Starting values.
INTEGER AF	!The "Add factor" to deviate from Fibonacci numbers.
OPTIONAL AF	!Indicate that this parameter may be omitted.
INTEGER EMBOLISM	!The bloat to employ.
INTEGER N,LN,LNL1,LNL2	!Assistants to the calculation.
IF (PRESENT(AF)) THEN	!Perhaps the last parameter has not been given.
EMBOLISM = AF			!It has. Take its value.
ELSE			!But if not,
EMBOLISM = 1			!This is the specified default.
END IF			!Perhaps there should be some report on this?
WRITE (6,1) LAST,L0,L1,EMBOLISM	!Announce.
1   FORMAT ("The first ",I0,	!The I0 format code avoids excessive spacing.
1   " numbers in the Leonardo sequence defined by L(0) = ",I0,
2   " and L(1) = ",I0," with L(n) = L(n - 1) + L(n - 2) + ",I0)
IF (LAST .GE. 1) WRITE (6,2) L0	!In principle, LAST may be small.
IF (LAST .GE. 2) WRITE (6,2) L1	!!So, suspicion rules.
2   FORMAT (I0,", ",\$)	!Obviously, the \$ sez "don't finish the line".
LNL1 = L0	!Syncopation for the sequence's initial values.
LN = L1		!Since the parameters ought not be damaged.
DO N = 3,LAST	!Step away.
LNL2 = LNL1		!Advance the two state variables one step.
LNL1 = LN		!Ready to make a step forward.
LN = LNL1 + LNL2 + EMBOLISM	!Thus.
WRITE (6,2) LN	!Reveal the value. Overflow is distant...
END DO		!On to the next step.
WRITE (6,*)	!Finish the line.
END SUBROUTINE LEONARDO	!Only speedy for the sequential production of values.

PROGRAM POKE

CALL LEONARDO(25,1,1,1)	!The first 25 Leonardo numbers.
CALL LEONARDO(25,0,1,0)	!Deviates to give the Fibonacci sequence.
END
```

Output:

```The first 25 numbers in the Leonardo sequence defined by L(0) = 1 and L(1) = 1 with L(n) = L(n - 1) + L(n - 2) + 1
1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049,
The first 25 numbers in the Leonardo sequence defined by L(0) = 0 and L(1) = 1 with L(n) = L(n - 1) + L(n - 2) + 0
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,
```

## FreeBASIC

```Sub leonardo(L0 As Integer, L1 As Integer, suma As Integer, texto As String)
Dim As Integer i, tmp
Print "Numeros de " &texto &" (" &L0 &"," &L1 &"," &suma &"):"
For i = 1 To 25
If i = 1 Then
Print L0;
Elseif i = 2 Then
Print L1;
Else
Print L0 + L1 + suma;
tmp = L0
L0 = L1
L1 = tmp + L1 + suma
End If
Next i
Print Chr(10)
End Sub

'--- Programa Principal ---
leonardo(1,1,1,"Leonardo")
leonardo(0,1,0,"Fibonacci")
End
```
Output:
```Numeros de Leonardo (1,1,1):
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Numeros de Fibonacci (0,1,0):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Go

```package main

import "fmt"

func leonardo(n, l0, l1, add int) []int {
leo := make([]int, n)
leo[0] = l0
leo[1] = l1
for i := 2; i < n; i++ {
leo[i] = leo[i - 1] + leo[i - 2] + add
}
return leo
}

func main() {
fmt.Println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
fmt.Println(leonardo(25, 1, 1, 1))
fmt.Println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
fmt.Println(leonardo(25, 0, 1, 0))
}
```
Output:
```The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
[1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049]

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
[0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368]
```

```import Data.List (intercalate, unfoldr)
import Data.List.Split (chunksOf)

--------------------- LEONARDO NUMBERS ---------------------
-- L0 -> L1 -> Add number -> Series (infinite)
leo :: Integer -> Integer -> Integer -> [Integer]
leo l0 l1 d = unfoldr (\(x, y) -> Just (x, (y, x + y + d))) (l0, l1)

leonardo :: [Integer]
leonardo = leo 1 1 1

fibonacci :: [Integer]
fibonacci = leo 0 1 0

--------------------------- TEST ---------------------------
main :: IO ()
main =
(putStrLn . unlines)
[ "First 25 default (1, 1, 1) Leonardo numbers:\n"
, f \$ take 25 leonardo
, "First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci numbers):\n"
, f \$ take 25 fibonacci
]
where
f = unlines . fmap (('\t' :) . intercalate ",") . chunksOf 16 . fmap show
```
Output:
```First 25 default (1, 1, 1) Leonardo numbers:

1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973
3193,5167,8361,13529,21891,35421,57313,92735,150049

First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci numbers):

0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610
987,1597,2584,4181,6765,10946,17711,28657,46368```

Alternately, defining the list self-referentially instead of using unfoldr:

```leo :: Integer -> Integer -> Integer -> [Integer]
leo l0 l1 d = s where
s = l0 : l1 : zipWith (\x y -> x + y + d) s (tail s)
```

## J

```leo =:  (] , {.@[ + _2&{@] + {:@])^:(_2&+@{:@[)
```
Output:
``` 1 25 leo 1 1
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

0 25 leo 0 1
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Java

Translation of: Kotlin
```import java.util.Arrays;
import java.util.List;

@SuppressWarnings("SameParameterValue")
public class LeonardoNumbers {
private static List<Integer> leonardo(int n) {
return leonardo(n, 1, 1, 1);
}

private static List<Integer> leonardo(int n, int l0, int l1, int add) {
Integer[] leo = new Integer[n];
leo[0] = l0;
leo[1] = l1;
for (int i = 2; i < n; i++) {
leo[i] = leo[i - 1] + leo[i - 2] + add;
}
return Arrays.asList(leo);
}

public static void main(String[] args) {
System.out.println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:");
System.out.println(leonardo(25));
System.out.println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:");
System.out.println(leonardo(25, 0, 1, 0));
}
}
```
Output:
```The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]```

## JavaScript

### ES6

```const leoNum = (c, l0 = 1, l1 = 1, add = 1) =>
(p, c, i) => i > 1 ? (
p.push(p[i - 1] + p[i - 2] + c) && p
) : p, [l0, l1]
);

console.log(leoNum(25));
console.log(leoNum(25, 0, 1, 0));
```
```[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]```

Or, taking N terms from a non-finite Javascript generator:

Translation of: Python
```(() => {
'use strict';

// leo :: Int -> Int -> Int -> Generator [Int]
function* leo(L0, L1, delta) {
let [x, y] = [L0, L1];
while (true) {
yield x;
[x, y] = [y, delta + x + y];
}
}

// ----------------------- TEST ------------------------
// main :: IO ()
const main = () => {
const
leonardo = leo(1, 1, 1),
fibonacci = leo(0, 1, 0);

return unlines([
'First 25 Leonardo numbers:',
indentWrapped(take(25)(leonardo)),
'',
'First 25 Fibonacci numbers:',
indentWrapped(take(25)(fibonacci))
]);
};

// -------------------- FORMATTING ---------------------

// indentWrapped :: [Int] -> String
const indentWrapped = xs =>
unlines(
map(x => '\t' + x.join(','))(
chunksOf(16)(
map(str)(xs)
)
)
);

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

// chunksOf :: Int -> [a] -> [[a]]
const chunksOf = n =>
xs => enumFromThenTo(0)(n)(
xs.length - 1
).reduce(
(a, i) => a.concat([xs.slice(i, (n + i))]),
[]
);

// enumFromThenTo :: Int -> Int -> Int -> [Int]
const enumFromThenTo = x1 =>
x2 => y => {
const d = x2 - x1;
return Array.from({
length: Math.floor(y - x2) / d + 2
}, (_, i) => x1 + (d * i));
};

// map :: (a -> b) -> [a] -> [b]
const map = f =>
// The list obtained by applying f
// to each element of xs.
// (The image of xs under f).
xs => [...xs].map(f);

// str :: a -> String
const str = x =>
x.toString();

// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = n =>
// The first n elements of a list,
// string of characters, or stream.
xs => 'GeneratorFunction' !== xs
.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));

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

// MAIN ---
return main();
})();
```
Output:
```First 25 Leonardo numbers:
1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973
3193,5167,8361,13529,21891,35421,57313,92735,150049

First 25 Fibonacci numbers:
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610
987,1597,2584,4181,6765,10946,17711,28657,46368```

## jq

### Naive Implementation

```def Leonardo(zero; one; incr):
def leo:
if . == 0 then zero
elif . == 1 then one
else ((.-1) |leo) + ((.-2) | leo) +  incr
end;
leo;```

### Implementation with Caching

An array is used for caching, with `.[n]` storing the value L(n).

```def Leonardo(zero; one; incr):
def leo(n):
if .[n] then .
else leo(n-1)   # optimization of leo(n-2)|leo(n-1)
| .[n] = .[n-1] + .[n-2] +  incr
end;
. as \$n | [zero,one] | leo(\$n) | .[\$n];```

(To compute the sequence of Leonardo numbers L(1) ... L(n) without redundant computation, the last element of the pipeline in the last line of the function above should be dropped.)

Examples

`[range(0;25) | Leonardo(1;1;1)]`
Output:
`[1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973,3193,5167,8361,13529,21891,35421,57313,92735,150049]`
`[range(0;25) | Leonardo(0;1;0)]`
Output:
`[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368]`

## Julia

Works with: Julia version 0.6
```function L(n, add::Int=1, firsts::Vector=[1, 1])
l = max(maximum(n) .+ 1, length(firsts))
r = Vector{Int}(l)
r[1:length(firsts)] = firsts
for i in 3:l
r[i] = r[i - 1] + r[i - 2] + add
end
return r[n .+ 1]
end

println("First 25 Leonardo numbers: ", join(L(0:24), ", "))

@show L(0) L(1)

println("First 25 Leonardo numbers starting with [0, 1]: ", join(L(0:24, 0, [0, 1]), ", "))
```
Output:
```First 25 Leonardo numbers: 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049
L(0) = 1
L(1) = 1
First 25 Leonardo numbers starting with 0, 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368```

## Kotlin

```// version 1.1.2

fun leonardo(n: Int, l0: Int = 1, l1: Int = 1, add: Int = 1): IntArray {
val leo = IntArray(n)
leo[0] = l0
leo[1] = l1
for (i in 2 until n) leo[i] = leo[i - 1] + leo[i - 2] + add
return leo
}

fun main(args: Array<String>) {
println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
println(leonardo(25).joinToString(" "))
println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
println(leonardo(25, 0, 1, 0).joinToString(" "))
}
```
Output:
```The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Lua

```function leoNums (n, L0, L1, add)
local L0, L1, add = L0 or 1, L1 or 1, add or 1
local lNums, nextNum = {L0, L1}
while #lNums < n do
nextNum = lNums[#lNums] + lNums[#lNums - 1] + add
table.insert(lNums, nextNum)
end
return lNums
end

function show (msg, t)
print(msg .. ":")
for i, x in ipairs(t) do
io.write(x .. " ")
end
print("\n")
end

show("Leonardo numbers", leoNums(25))
show("Fibonacci numbers", leoNums(25, 0, 1, 0))
```
Output:
```Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368```

## Maple

```L := proc(n, L_0, L_1, add)
if n = 0 then
return L_0;
elif n = 1 then
return L_1;
else
return L(n - 1) + L(n - 2) + add;
end if;
end proc:

Leonardo := n -> (L(1, 1, 1),[seq(0..n - 1)])

Fibonacci := n -> (L(0, 1, 0), [seq(0..n - 1)])```
```[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]```

## Mathematica/Wolfram Language

```L[0,L0_:1,___]:=L0
L[1,L0_:1,L1_:1,___]:=L1

L/@(Range[25]-1)
L[#,0,1,0]&/@(Range[25]-1)
```
```{1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049}
{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368}```

## min

Works with: min version 0.19.3
```(over over + rolldown pop pick +) :next
(('print dip " " print! next) 25 times newline) :leo

"First 25 Leonardo numbers:" puts!
1 1 1 leo
"First 25 Leonardo numbers with add=0, L(0)=0, L(1)=1:" puts!
0 0 1 leo```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with add=0, L(0)=0, L(1)=1:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Modula-2

```MODULE Leonardo;
FROM FormatString IMPORT FormatString;

PROCEDURE leonardo(a,b,step,num : INTEGER);
VAR
buf : ARRAY[0..63] OF CHAR;
i,temp : INTEGER;
BEGIN
FOR i:=1 TO num DO
IF i=1 THEN
FormatString(" %i", buf, a);
WriteString(buf)
ELSIF i=2 THEN
FormatString(" %i", buf, b);
WriteString(buf)
ELSE
FormatString(" %i", buf, a+b+step);
WriteString(buf);

temp := a;
a := b;
b := temp + b + step
END
END;
WriteLn
END leonardo;

BEGIN
leonardo(1,1,1,25);
leonardo(0,1,0,25);

END Leonardo.
```

## Nim

```import strformat

proc leonardoNumbers(count: int, L0: int = 1,
L1: int = 1, ADD: int = 1) =
var t = 0
var (L0_loc, L1_loc) = (L0, L1)
for i in 0..<count:
write(stdout, fmt"{L0_loc:7}")
t = L0_loc + L1_loc + ADD
L0_loc = L1_loc
L1_loc = t
if i mod 5 == 4:
write(stdout, "\n")
write(stdout, "\n")

echo "Leonardo Numbers:"
leonardoNumbers(25)
echo "Fibonacci Numbers: "
leonardoNumbers(25, 0, 1, 0)
```
Output:
```Leonardo Numbers:
1      1      3      5      9
15     25     41     67    109
177    287    465    753   1219
1973   3193   5167   8361  13529
21891  35421  57313  92735 150049

Fibonacci Numbers:
0      1      1      2      3
5      8     13     21     34
55     89    144    233    377
610    987   1597   2584   4181
6765  10946  17711  28657  46368
```

## OCaml

```let seq_leonardo i =
let rec next b a () = Seq.Cons (a, next (a + b + i) b) in
next

let () =
let show (s, a, b, i) =
seq_leonardo i b a |> Seq.take 25
|> Seq.fold_left (Printf.sprintf "%s %u") (Printf.sprintf "First 25 %s numbers:\n" s)
|> print_endline
in
List.iter show ["Leonardo", 1, 1, 1; "Fibonacci", 0, 1, 0]
```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Perl

```no warnings 'experimental::signatures';
use feature 'signatures';

sub leonardo (\$n, \$l0 = 1, \$l1 = 1, \$add = 1) {
(\$l0, \$l1) = (\$l1, \$l0+\$l1+\$add)  for 1..\$n;
\$l0;
}

my @L = map { leonardo(\$_) } 0..24;
print "Leonardo[1,1,1]: @L\n";
my @F = map { leonardo(\$_,0,1,0) } 0..24;
print "Leonardo[0,1,0]: @F\n";
```
Output:
```Leonardo[1,1,1]: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Leonardo[0,1,0]: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Phix

```with javascript_semantics
function leonardo(integer n, l1=1, l2=1, step=1)
-- return the first n leonardo numbers, starting {l1,l2}, with step as the add number
sequence res = {l1,l2}
while length(res)<n do
res = append(res,res[\$]+res[\$-1]+step)
end while
return res
end function
?{"Leonardo",leonardo(25)}
?{"Fibonacci",leonardo(25,0,1,0)}
```
Output:
```{"Leonardo",{1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973,3193,5167,8361,13529,21891,35421,57313,92735,150049}}
{"Fibonacci",{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368}}
```

## Picat

```go =>
println([leonardo(I) : I in 0..24]),
println([leonardo(0,1,0,I) : I in 0..24]).

leonardo(N) = leonardo(1,1,1,N).
table
Output:
```[1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973,3193,5167,8361,13529,21891,35421,57313,92735,150049]
[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368]```

## PicoLisp

```(de leo (A B C)
(default A 1  B 1  C 1)
(make
(do 25
(inc
'B
(+ (link (swap 'A B)) C) ) ) ) )

(println 'Leonardo (leo))
(println 'Fibonacci (leo 0 1 0))```
Output:
```Leonardo (1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049)
Fibonacci (0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368)```

## Plain English

```To run:
Start up.
Write "First 25 Leonardo numbers:" on the console.
Show 25 of the Leonardo numbers starting with 1 and 1 and using 1 for the add number.
Write "First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:" on the console.
Show 25 of the Leonardo numbers starting with 0 and 1 and using 0 for the add number.
Wait for the escape key.
Shut down.

To show a number of the Leonardo numbers starting with a first number and a second number and using an add number for the add number:
If the number is less than 2, exit.
Privatize the number.
Privatize the first number.
Privatize the second number.
Subtract 2 from the number.
Write the first number then " " then the second number on the console without advancing.
Loop.
If a counter is past the number, write "" on the console; exit.
Swap the first number with the second number.
Put the first number plus the second number plus the add number into the second number.
Write the second number then " " on the console without advancing.
Repeat.```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## PureBasic

```EnableExplicit

#N = 25

Procedure leon_R(a.i, b.i, s.i = 1, n.i = #N)

If n>2
Print(Space(1) + Str(a + b + s))
ProcedureReturn leon_R(b, a + b + s, s, n-1)
EndIf

EndProcedure

If OpenConsole()

Define r\$

Print("Enter first two Leonardo numbers and increment step (separated by space) : ")
r\$ = Input()
PrintN("First " + Str(#N) + " Leonardo numbers : ")
Print(StringField(r\$, 1, Chr(32)) + Space(1) +
StringField(r\$, 2, Chr(32)))

leon_R(Val(StringField(r\$, 1, Chr(32))),
Val(StringField(r\$, 2, Chr(32))),
Val(StringField(r\$, 3, Chr(32))))

r\$ = Input()
EndIf
```
Output:
```Enter first two Leonardo numbers and increment step (separated by space) : 1 1 1
First 25 Leonardo numbers :
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Enter first two Leonardo numbers and increment step (separated by space) : 0 1 0
First 25 Leonardo numbers :
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Python

### Finite iteration

```def Leonardo(L_Zero, L_One, Add, Amount):
terms = [L_Zero,L_One]
while len(terms) < Amount:
new = terms[-1] + terms[-2]
terms.append(new)
return terms

out = ""
print "First 25 Leonardo numbers:"
for term in Leonardo(1,1,1,25):
out += str(term) + " "
print out

out = ""
print "Leonardo numbers with fibonacci parameters:"
for term in Leonardo(0,1,0,25):
out += str(term) + " "
print out
```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Leonardo numbers with fibonacci parameters:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

### Non-finite generation

Or, for a non-finite stream of Leonardos, we can use a Python generator:

Works with: Python version 3
```'''Leonardo numbers'''

from functools import (reduce)
from itertools import (islice)

# leo :: Int -> Int -> Int -> Generator [Int]
def leo(L0, L1, delta):
'''A number series of the
Leonardo and Fibonacci pattern,
where L0 and L1 are the first two terms,
and delta = 1 for (L0, L1) == (1, 1)
yields the Leonardo series, while
delta = 0 defines the Fibonacci series.'''
(x, y) = (L0, L1)
while True:
yield x
(x, y) = (y, x + y + delta)

# main :: IO()
def main():
'''Tests.'''

print('\n'.join([
'First 25 Leonardo numbers:',
folded(16)(take(25)(
leo(1, 1, 1)
)),
'',
'First 25 Fibonacci numbers:',
folded(16)(take(25)(
leo(0, 1, 0)
))
]))

# FORMATTING ----------------------------------------------

# folded :: Int -> [a] -> String
def folded(n):
'''Long list folded to rows of n terms each.'''
return lambda xs: '[' + ('\n '.join(
str(ns)[1:-1] for ns in chunksOf(n)(xs)
) + ']')

# GENERIC -------------------------------------------------

# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n,
subdividing the contents of xs.
Where the length of xs is not evenly divible,
the final list will be shorter than n.'''
return lambda xs: reduce(
lambda a, i: a + [xs[i:n + i]],
range(0, len(xs), n), []
) if 0 < n else []

# 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))
)

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```First 25 Leonardo numbers:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973
3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

First 25 Fibonacci numbers:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]```

## Quackery

```  [ 1 1 1 ]             is leo     (         --> n n n )

[ 0 1 0 ]             is fibo    (         --> n n n )

[ 2 1 0 ]             is lucaso (         --> n n n )

[ temp put
rot times
[ tuck +
temp share + ]
temp release drop ] is nardo   ( n n n n --> n     )

say "Leonardo numbers:" cr
25 times [ i^ leo nardo echo sp ]
cr cr
say "Fibonacci numbers:" cr
25 times [ i^ fibo nardo echo sp ]
cr cr
say "Lucas numbers:" cr
25 times [ i^ lucaso nardo echo sp ]```
Output:
```Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Lucas numbers:
2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682
```

## R

```leonardo_numbers <- function(add = 1, l0 = 1, l1 = 1, how_many = 25) {
result <- c(l0, l1)
for (i in 3:how_many)
result <- append(result, result[[i - 1]] + result[[i - 2]] + add)
result
}
cat("First 25 Leonardo numbers\n")
cat(leonardo_numbers(), "\n")

cat("First 25 Leonardo numbers from 0, 1 with add number = 0\n")
cat(leonardo_numbers(0, 0, 1), "\n")
```
Output:
```First 25 Leonardo numbers
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers from 0, 1 with add number = 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Racket

```#lang racket
(define (Leonardo n #:L0 (L0 1) #:L1 (L1 1) #:1+ (1+ 1))
(cond [(= n 0) L0]
[(= n 1) L1]
[else
(let inr ((n (- n 2)) (L_n-2 L0) (L_n-1 L1))
(let ((L_n (+ L_n-1 L_n-2 1+)))
(if (zero? n) L_n (inr (sub1 n) L_n-1 L_n))))]))

(module+ main
(map Leonardo (range 25))
(map (curry Leonardo #:L0 0 #:L1 1 #:1+ 0) (range 25)))

(module+ test
(require rackunit)
(check-equal? (Leonardo 0) 1)
(check-equal? (Leonardo 1) 1)
(check-equal? (Leonardo 2) 3)
(check-equal? (Leonardo 3) 5))
```
Output:
```'(1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049)
'(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368)```

## Raku

(formerly Perl 6)

```sub 𝑳 ( \$𝑳0 = 1, \$𝑳1 = 1, \$𝑳add = 1 ) { \$𝑳0, \$𝑳1, { \$^n2 + \$^n1 + \$𝑳add } ... * }

# Part 1
say "The first 25 Leonardo numbers:";
put 𝑳()[^25];

# Part 2
say "\nThe first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:";
put 𝑳( 0, 1, 0 )[^25];
```
Output:
```The first 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368```

## REXX

```/*REXX pgm computes Leonardo numbers, allowing the specification of L(0), L(1), and ADD#*/
numeric digits 500                               /*just in case the user gets ka-razy.  */
@.=1                                             /*define the default for the  @. array.*/
parse arg N L0 L1 a# .                           /*obtain optional arguments from the CL*/
if  N =='' |  N ==","  then    N= 25             /*Not specified?  Then use the default.*/
if L0\=='' & L0\==","  then  @.0= L0             /*Was     "         "   "   "   value. */
if L1\=='' & L1\==","  then  @.1= L1             /* "      "         "   "   "     "    */
if a#\=='' & a#\==","  then  @.a= a#             /* "      "         "   "   "     "    */
say 'The first '   N   " Leonardo numbers are:"  /*display a title for the output series*/
if @.0\==1 | @.1\==1  then say 'using '     @.0     " for L(0)"
if @.0\==1 | @.1\==1  then say 'using '     @.1     " for L(1)"
if @.a\==1            then say 'using '     @.a     " for the  add  number"
say                                              /*display blank line before the output.*/
\$=                                               /*initialize the output line to "null".*/
do j=0  for N                       /*construct a list of Leonardo numbers.*/
if j<2  then z=@.j                  /*for the 1st two numbers, use the fiat*/
else do                     /*··· otherwise, compute the Leonardo #*/
_=@.0                  /*save the old primary Leonardo number.*/
@.0=@.1                /*store the new primary number in old. */
@.1=@.0  +  _  +  @.a  /*compute the next Leonardo number.    */
z=@.1                  /*store the next Leonardo number in Z. */
end                    /* [↑]  only 2 Leonardo #s are stored. */
\$=\$ z                               /*append the just computed # to \$ list.*/
end   /*j*/                         /* [↓]  elide the leading blank in  \$. */
say strip(\$)                                     /*stick a fork in it,  we're all done. */
```
output   when using the default input:
```The first  25  Leonardo numbers are:

1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
```
output   when using the input of:     12   0   1   0
```The first  25  Leonardo numbers are:
using  0  for L(0)
using  1  for L(1)
using  0  for the  add  number

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Ring

```# Project : Leanardo numbers

n0 = 1
n1 = 1
see "First 25 Leonardo numbers:" + nl
leonardo()
n0 = 1
n1 = 1
see "First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):" + nl
see "" + add + " "
leonardo()

func leonardo()
see "" + n0 + " " + n1
for i=3 to 25
temp=n1
n0=temp
see " "+ n1
next
see nl```

Output:

```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025
```

## RPL

Works with: Halcyon Calc version 4.2.7
```≪ → l0 l1 add n
≪ l0 l1 2 →LIST
IF n 3 ≥
THEN
l0 l1 2 n 1 - START
ROT OVER + 3 ROLLD
NEXT DROP2
END
≫ ≫ 'LENDO' STO
```
```( L(0) L(1) add n -- { L(0) .. L(n-1) } )
Initialize sequence

Initialise stack and loop
Calculate next L(i)
Store it into sequence list
Clean stack

```

The following instructions will deliver what is required:

```1 1 1 25 LENDO
0 1 0 25 LENDO
```
Output:
```2: { 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 }
1: { 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 }
```

## Ruby

Enumerators are nice for this.

```def leonardo(l0=1, l1=1, add=1)
loop do
yield l0
end
end

p leonardo.take(25)
p leonardo(0,1,0).take(25)
```
Output:
```[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]
```

## Run BASIC

```sqliteconnect #mem, ":memory:"
#mem execute("INSERT INTO lno VALUES('Leonardo',1,1,1),('Fibonacci',0,1,0);")
#mem execute("SELECT * FROM lno")
for j = 1 to 2
#row  = #mem #nextrow()
name\$ = #row name\$()
L0    = #row L0()
L1    = #row L1()
for i = 3 to 25
temp  = L1
L1    = L0 + L1 + ad
L0    = temp
print L1;" ";
next i
next j
end```
```Leonardo add=1
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Rust

```fn leonardo(mut n0: u32, mut n1: u32, add: u32) -> impl std::iter::Iterator<Item = u32> {
std::iter::from_fn(move || {
let n = n0;
n0 = n1;
Some(n)
})
}

fn main() {
println!("First 25 Leonardo numbers:");
for i in leonardo(1, 1, 1).take(25) {
print!("{} ", i);
}
println!();
println!("First 25 Fibonacci numbers:");
for i in leonardo(0, 1, 0).take(25) {
print!("{} ", i);
}
println!();
}
```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Scala

```def leo( n:Int, n1:Int=1, n2:Int=1, addnum:Int=1 ) : BigInt = n match {
case 0 => n1
case 1 => n2
case n => leo(n - 1, n1, n2, addnum) + leo(n - 2, n1, n2, addnum) + addnum
}

{
println( "The first 25 Leonardo Numbers:")
(0 until 25) foreach { n => print( leo(n) + " " ) }

println( "\n\nThe first 25 Fibonacci Numbers:")
(0 until 25) foreach { n => print( leo(n, n1=0, n2=1, addnum=0) + " " ) }
}
```
Output:
```The first 25 Leonardo Numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Fibonacci Numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Seed7

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

const proc: leonardo (in var integer: l0, in var integer: l1, in integer: add, in integer: count) is func
local
var integer: temp is 0;
begin
for count do
write(" " <& l0);
temp := l0 + l1 + add;
l0 := l1;
l1 := temp;
end for;
writeln;
end func;

const proc: main is func
begin
write("Leonardo Numbers:");
leonardo(1, 1, 1, 25);
write("Fibonacci Numbers:");
leonardo(0, 1, 0, 25);
end func;```
Output:
```Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Sidef

```func 𝑳(n, 𝑳0 = 1, 𝑳1 = 1, 𝑳add = 1) {
{ (𝑳0, 𝑳1) = (𝑳1, 𝑳0 + 𝑳1 + 𝑳add) } * n
return 𝑳0
}

say "The first 25 Leonardo numbers:"
say 25.of { 𝑳(_) }

say "\nThe first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:"
say 25.of { 𝑳(_, 0, 1, 0) }
```
Output:
```The first 25 Leonardo numbers:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

The first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]
```

## Swift

```struct Leonardo: Sequence, IteratorProtocol {
private var n0: Int
private var n1: Int

init(n0: Int = 1, n1: Int = 1, add: Int = 1) {
self.n0 = n0
self.n1 = n1
}

mutating func next() -> Int? {
let n = n0
n0 = n1
return n
}
}

print("First 25 Leonardo numbers:")
print(Leonardo().prefix(25).map{String(\$0)}.joined(separator: " "))

print("First 25 Fibonacci numbers:")
print(Leonardo(n0: 0, add: 0).prefix(25).map{String(\$0)}.joined(separator: " "))
```
Output:
```First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## VBA

```Option Explicit

Private Sub LeonardoNumbers()
Dim L, MyString As String
Debug.Print "First 25 Leonardo numbers :"
L = Leo_Numbers(25, 1, 1, 1)
MyString = Join(L, "; ")
Debug.Print MyString
Debug.Print "First 25 Leonardo numbers from 0, 1 with add number = 0"
L = Leo_Numbers(25, 0, 1, 0)
MyString = Join(L, "; ")
Debug.Print MyString
Debug.Print "If the first prarameter is too small :"
L = Leo_Numbers(1, 0, 1, 0)
MyString = Join(L, "; ")
Debug.Print MyString
End Sub

Public Function Leo_Numbers(HowMany As Long, L_0 As Long, L_1 As Long, Add_Nb As Long)
Dim N As Long, Ltemp

If HowMany > 1 Then
ReDim Ltemp(HowMany - 1)
Ltemp(0) = L_0: Ltemp(1) = L_1
For N = 2 To HowMany - 1
Ltemp(N) = Ltemp(N - 1) + Ltemp(N - 2) + Add_Nb
Next N
Else
ReDim Ltemp(0)
Ltemp(0) = "The first parameter is too small"
End If
Leo_Numbers = Ltemp
End Function
```
Output:
```First 25 Leonardo numbers :
1; 1; 3; 5; 9; 15; 25; 41; 67; 109; 177; 287; 465; 753; 1219; 1973; 3193; 5167; 8361; 13529; 21891; 35421; 57313; 92735; 150049
First 25 Leonardo numbers from 0, 1 with add number = 0
0; 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610; 987; 1597; 2584; 4181; 6765; 10946; 17711; 28657; 46368
If the first prarameter is too small :
The first parameter is too small```

## Visual Basic .NET

Translation of: C#
```Module Module1

Iterator Function Leonardo(Optional L0 = 1, Optional L1 = 1, Optional add = 1) As IEnumerable(Of Integer)
While True
Yield L0
Dim t = L0 + L1 + add
L0 = L1
L1 = t
End While
End Function

Sub Main()
Console.WriteLine(String.Join(" ", Leonardo().Take(25)))
Console.WriteLine(String.Join(" ", Leonardo(0, 1, 0).Take(25)))
End Sub

End Module
```
Output:
```1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368```

## V (Vlang)

Translation of: go
```fn leonardo(n int, l0 int, l1 int, add int) []int {
mut leo := []int{len: n}
leo[0] = l0
leo[1] = l1
for i := 2; i < n; i++ {
leo[i] = leo[i - 1] + leo[i - 2] + add
}
return leo
}

fn main() {
println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
println(leonardo(25, 1, 1, 1))
println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
println(leonardo(25, 0, 1, 0))
}```
Output:
```The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]
```

## Wren

```var leonardo = Fn.new { |first, add, limit|
var leo = List.filled(limit, 0)
leo[0] = first[0]
leo[1] = first[1]
for (i in 2...limit) leo[i] = leo[i-1] + leo[i-2] + add
return leo
}

System.print("The first 25 Leonardo numbers with L(0) = 1, L(1) = 1 and Add = 1 are:")
for (l in leonardo.call([1, 1], 1, 25)) System.write("%(l) ")

System.print("\n\nThe first 25 Leonardo numbers with L(0) = 0, L(1) = 1 and Add = 0 are:")
for (l in leonardo.call([0, 1], 0, 25)) System.write("%(l) ")
System.print()
```
Output:
```The first 25 Leonardo numbers with L(0) = 1, L(1) = 1 and Add = 1 are:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Leonardo numbers with L(0) = 0, L(1) = 1 and Add = 0 are:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## Yabasic

```limit = 25

sub leonardo(L0, L1, suma, texto\$)
local i
print "Numeros de " + texto\$, " (", L0, ",", L1, ",", suma, "):"
for i = 1 to limit
if i = 1 then print L0, " ";
elsif i = 2 then print L1, " ";
else
print L0 + L1 + suma, " ";
tmp = L0
L0 = L1
L1 = tmp + L1 + suma
endif
next i
print chr\$(10)
end sub

leonardo(1,1,1,"Leonardo")
leonardo(0,1,0,"Fibonacci")
end```

## XPL0

```int N, L, L0, L1, Add;
[Text(0, "Enter L(0), L(1), Add: ");
L0:= IntIn(0);
L1:= IntIn(0);
IntOut(0, L0);  ChOut(0, ^ );
IntOut(0, L1);  ChOut(0, ^ );
for N:= 3 to 25 do
[L:= L1 + L0 + Add;
IntOut(0, L);  ChOut(0, ^ );
L0:= L1;
L1:= L;
];
]```
Output:
```Enter L(0), L(1), Add: 1 1 1
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Enter L(0), L(1), Add: 0 1 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```

## zkl

```fcn leonardoNumber(n, n1=1,n2=1,addnum=1){
if(n==0) return(n1);
if(n==1) return(n2);
}```
```println("The first 25 Leonardo Numbers:");
foreach n in (25){ print(leonardoNumber(n)," ") }
println("\n");

println("The first 25 Fibonacci Numbers:");
foreach n in (25){ print(leonardoNumber(n, 0,1,0)," ") }
println();```
Output:
```The first 25 Leonardo Numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Fibonacci Numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368
```