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[[Category:Classic CS problems and programs]]
 
<!-- The following <math> tag doesn't render properly as it does correctly on Wikipedia.
<!-- Leonardo numbers are also known as the Leonardo series. -->
It generates some bold red error messages.
 
<!-- The following <math> tag doesn't render properly as it does correctly on Wikipedia:.
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
:<math>
L(n) =
\begin{cases}
Line 17:
</math>
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-->
 
(end of comment) -->
The &nbsp; '''Leonardo numbers''' &nbsp; are a sequence of numbers defined by:
<big>
 
''Leonardo numbers'' &nbsp; are also known as the &nbsp; ''Leonardo series''.
L(0) = 1
L(1) = 1
L(n) = L(n-1) + L(n-2) + 1
also
L(n) = 2 * Fib(n+1) - 1
 
</big>
::: &nbsp; where the &nbsp; '''+ 1''' &nbsp; will herein be known as the &nbsp; ''add'' &nbsp; number.
::: &nbsp; where the &nbsp; '''FIB''' &nbsp; is the &nbsp; [[wp:Fibonacci number|Fibonacci number]]s.
 
The &nbsp; '''Leonardo numbers''' &nbsp; are a sequence of numbers defined by:
<big> L(0) = 1 [1<sup>st</sup> equation] </big>
<big> L(1) = 1 [2<sup>nd</sup> equation] </big>
<big> L(n) = L(n-1) + L(n-2) + 1 [3<sup>rd</sup> equation] </big>
─── also ───
<big> L(n) = 2 * Fib(n+1) - 1 [4<sup>th</sup> equation] </big>
 
:::: &nbsp; where the &nbsp; '''+ 1''' &nbsp; will herein be known as the &nbsp; ''add'' &nbsp; number.
The task will be using the 3<sup>rd</sup> equation (above) to calculate the Leonardo numbers.
:::: &nbsp; where the &nbsp; '''FIB''' &nbsp; is the &nbsp; [[wp:Fibonacci number|Fibonacci number]]s.
 
 
This task will be using the 3<sup>rd</sup> equation (above) to calculate the Leonardo numbers.
[[wp:Edsger W. Dijkstra|Edsger W. Dijkstra]] &nbsp; used them as an integral part of
 
 
[[wp:Edsger W. Dijkstra|Edsger W. Dijkstra]] &nbsp; used &nbsp; Leonardo numbers &nbsp; as an integral part of
his &nbsp; [[wp:smoothsort|smoothsort]] &nbsp; [[wp:algorithm|algorithm]].
 
Line 62 ⟶ 63:
 
 
Show all output here on this page.
 
 
Line 75 ⟶ 76:
* &nbsp; [[oeis:A001595|OEIS Leonardo numbers]]
<br><br>
 
=={{header|11l}}==
{{trans|C++}}
 
<syntaxhighlight lang="11l">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)</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|Action!}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Leonardo_numbers.png Screenshot from Atari 8-bit computer]
<pre>
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
</pre>
 
=={{header|Ada}}==
<syntaxhighlight lang="ada">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;</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|ALGOL 68}}==
<langsyntaxhighlight lang="algol68">BEGIN
# leonardo number parameters #
MODE LEONARDO = STRUCT( INT l0, l1, add number );
Line 118 ⟶ 231:
show( 25, leonardo numbers WITHLZERO 0 WITHADDNUMBER 0 );
print( ( newline ) )
END</langsyntaxhighlight>
{{out}}
<pre>
Line 124 ⟶ 237:
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
</pre>
 
=={{header|AppleScript}}==
===Functional===
{{Trans|Python}} (Generator version)
 
 
Drawing N items from a non-finite generator:
<syntaxhighlight lang="applescript">------------------------ 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</syntaxhighlight>
{{Out}}
<pre>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</pre>
----
===Idiomatic===
Allowing optional 'L0', 'L1', and/or 'add' specs with any version of AppleScript.
<syntaxhighlight lang="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.
set {L0:a, L1:b, add:inc} to spec & {L0:1, L1:1, add:1}
-- 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</syntaxhighlight>
 
{{output}}
<syntaxhighlight lang="applescript">"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"</syntaxhighlight>
 
=={{header|Arturo}}==
 
<syntaxhighlight lang="rebol">L: function [n l0 l1 ladd].memoize[
(n=0)? -> l0 [
(n=1)? -> l1
-> (L n-1 l0 l1 ladd) + (L n-2 l0 l1 ladd) + ladd
]
]
 
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</syntaxhighlight>
 
{{out}}
 
<pre>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</pre>
 
=={{header|AutoHotkey}}==
<syntaxhighlight lang="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
}</syntaxhighlight>
Examples:<syntaxhighlight lang="autohotkey">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</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|AWK}}==
<syntaxhighlight lang="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")
}
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Bash}}==
<syntaxhighlight lang="bash">
#!/bin/bash
 
function leonardo_number () {
L0_value=${2:-1}
L1_value=${3:-1}
Add=${4:-1}
leonardo_numbers=($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[*]}"
}
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|BASIC}}==
==={{header|BASIC256}}===
<syntaxhighlight lang="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
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
==={{header|IS-BASIC}}===
<syntaxhighlight lang="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
140 LET T=L1:LET L1=L1+L0+ADD:LET L0=T
160 PRINT L1;
170 NEXT
180 PRINT</syntaxhighlight>
 
==={{header|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.
<langsyntaxhighlight lang="basic"> 10 INPUT L0
20 INPUT L1
30 INPUT ADD
Line 139 ⟶ 627:
80 LET L0=TEMP
90 PRINT " ";L1;
100 NEXT I</langsyntaxhighlight>
{{in}}
<pre>1
Line 152 ⟶ 640:
{{out}}
<pre> 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</pre>
 
=={{header|BBC BASIC}}==
It's a shame when fonts don't make much of a distinction between <tt>l</tt> lower-case L and <tt>1</tt> the number One.
<syntaxhighlight lang="bbcbasic">REM >leonardo
:
PRINT "Enter values of L0, L1, and ADD, separated by commas:"
INPUT l0%, l1%, add%
PRINT l0% ' l1%
FOR i% = 3 TO 25
temp% = l1%
l1% += l0% + add%
l0% = temp%
PRINT l1%
NEXT
PRINT
END</syntaxhighlight>
{{out}}
<pre>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</pre>
<pre>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</pre>
 
=={{header|Burlesque}}==
<syntaxhighlight lang="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</syntaxhighlight>
 
=={{header|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.
<syntaxhighlight lang="c">
<lang C>
/*Abhishek Ghosh, 23rd September 2017*/
 
#include<stdio.h>
 
Line 192 ⟶ 756:
return 0;
}
</syntaxhighlight>
</lang>
Output :
Normal Leonardo Series :
Line 206 ⟶ 770:
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
</pre>
 
=={{header|C sharp}}==
{{works with|C sharp|7}}
<syntaxhighlight lang="csharp">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);
}
}
}</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|C++}}==
<langsyntaxhighlight lang="cpp">
#include <iostream>
 
Line 222 ⟶ 812:
return 0;
}
</syntaxhighlight>
</lang>
{{out}}<pre>
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
</pre>
 
=={{header|Common Lisp}}==
<syntaxhighlight lang="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.
;;; add is the "add number" as defined in the task definition.
;;;
 
(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))))))
</syntaxhighlight>
 
{{out}}
<pre>
> (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)
</pre>
 
=={{header|Crystal}}==
{{trans|Python}}
<syntaxhighlight lang="ruby">def leonardo(l_zero, l_one, add, amount)
terms = [l_zero, l_one]
while terms.size < amount
new = terms[-1] + terms[-2]
new += add
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) }"
</syntaxhighlight>
{{out}}
<pre>
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]
</pre>
 
=={{header|D}}==
{{trans|C++}}
<syntaxhighlight lang="d">
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();
}
</syntaxhighlight>
{{out}}<pre>
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
</pre>
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
 
 
<syntaxhighlight lang="Delphi">
type TIntArray = array of integer;
 
function GetLeonardoNumbers(Cnt,SN1,SN2,Add: integer): TIntArray;
var N: integer;
begin
SetLength(Result,Cnt);
Result[0]:=SN1; Result[1]:=SN2;
for N:=2 to Cnt-1 do
begin
Result[N]:=Result[N-1] + Result[N-2] + Add;
end;
end;
 
 
procedure TestLeonardoNumbers(Memo: TMemo);
var IA: TIntArray;
var S: string;
var I: integer;
begin
Memo.Lines.Add('Leonardo Numbers:');
IA:=GetLeonardoNumbers(25,1,1,1);
S:='';
for I:=0 to High(IA) do
begin
S:=S+' '+Format('%6d',[IA[I]]);
if I mod 5 = 4 then S:=S+#$0D#$0A;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('Fibonacci Numbers:');
IA:=GetLeonardoNumbers(25,0,1,0);
S:='';
for I:=0 to High(IA) do
begin
S:=S+' '+Format('%6d',[IA[I]]);
if I mod 5 = 4 then S:=S+#$0D#$0A;
end;
Memo.Lines.Add(S);
end;
 
 
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
proc leonardo L0 L1 add . .
print "L0:" & L0 & " L1:" & L1 & " add:" & add
write L0 & " "
write L1 & " "
for i = 2 to 24
tmp = L0
L0 = L1
L1 = tmp + L1 + add
write L1 & " "
.
print ""
.
leonardo 1 1 1
leonardo 0 1 0
</syntaxhighlight>
 
=={{header|EMal}}==
<syntaxhighlight lang="emal">
fun leonardo = List by int n, int leo0, int leo1, int add
List leo = int[].with(n)
leo[0] = leo0
leo[1] = leo1
for int i = 2; i < n; ++i
leo[i] = leo[i - 1] + leo[i - 2] + add
end
return leo
end
writeLine("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
writeLine(leonardo(25, 1, 1, 1))
writeLine()
writeLine("The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
writeLine(leonardo(25, 0, 1, 0))
</syntaxhighlight>
{{out}}
<pre>
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]
</pre>
 
=={{header|F#|F sharp}}==
{{trans|Haskell}}
<syntaxhighlight lang="fsharp">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</syntaxhighlight>
{{out}}
<pre>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|]]</pre>
 
=={{header|Factor}}==
<syntaxhighlight lang="text">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</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Fermat}}==
<syntaxhighlight lang="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
leo[1,i]:=leo[1,i-2]+leo[1,i-1]+add;
od;
.;
 
Leonardo(25, 1, 1, 1);
[leo];
 
Leonardo(25, 0, 1, 0);
[leo];</syntaxhighlight>
{{out}}
<pre>[[ 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 ]]
</pre>
 
Line 232 ⟶ 1,082:
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. <code>END SUBROUTINE LEONARDO</code> rather than just <code>END</code>) 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 <code>INTEGER, OPTIONAL:: AF</code> rather than two statements concerning AF. However, in a test run with <code>CALL LEONARDO(25,1,1)</code> 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 werewould 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. <langsyntaxhighlight Fortranlang="fortran"> SUBROUTINE LEONARDO(LAST,L0,L1,AF) !Show the first LAST values of the sequence.
INTEGER LAST !Limit to show.
INTEGER L0,L1 !Starting values.
Line 268 ⟶ 1,118:
CALL LEONARDO(25,1,1,1) !The first 25 Leonardo numbers.
CALL LEONARDO(25,0,1,0) !Deviates to give the Fibonacci sequence.
END </langsyntaxhighlight>
Output:
<pre>
Line 275 ⟶ 1,125:
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,
</pre>
 
=={{header|FreeBASIC}}==
<syntaxhighlight lang="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
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
local fn LeoFiboNumbers( number as long, l0 as long, l1 as long, sum as long ) as CFArrayRef
long i, tmp
CFMutableArrayRef mutArr = fn MutableArrayWithCapacity(0)
for i = 1 to number
if i = 1
MutableArrayAddObject( mutArr, fn StringWithFormat( @"%ld", l0 ) )
else
if i = 2
MutableArrayAddObject( mutArr, fn StringWithFormat( @"%ld", l1 ) )
else
MutableArrayAddObject( mutArr, fn StringWithFormat( @"%ld", l0 + l1 + sum ) )
tmp = L0 : l0 = l1 : l1 = tmp + l1 + sum
end if
end if
next
end fn = mutArr
 
void local fn CompareResults( number as long )
CFArrayRef leonardoArr = fn LeoFiboNumbers( number, 1, 1, 1 )
CFArrayRef fibonacciArr = fn LeoFiboNumbers( number, 0, 1, 0 )
long i, count = fn ArrayCount( leonardoArr )
printf @"First %ld numbers of:\n%8s%11s", number, fn StringUTF8String( @"Leonardo" ), fn StringUTF8String( @"Fibonacci" )
for i = 0 to count - 1
printf @"%8s%11s", fn StringUTF8String( leonardoArr[i] ), fn StringUTF8String( fibonacciArr[i] )
next
end fn
 
fn CompareResults( 35 )
 
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
First 35 numbers of:
Leonardo Fibonacci
1 0
1 1
3 1
5 2
9 3
15 5
25 8
41 13
67 21
109 34
177 55
287 89
465 144
753 233
1219 377
1973 610
3193 987
5167 1597
8361 2584
13529 4181
21891 6765
35421 10946
57313 17711
92735 28657
150049 46368
242785 75025
392835 121393
635621 196418
1028457 317811
1664079 514229
2692537 832040
4356617 1346269
7049155 2178309
11405773 3524578
18454929 5702887
</pre>
 
 
=={{header|Go}}==
<syntaxhighlight lang="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))
}</syntaxhighlight>
 
{{out}}
<pre>
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]
</pre>
 
=={{header|Haskell}}==
<langsyntaxhighlight Haskelllang="haskell">import Data.List.Split (chunksOfintercalate, unfoldr)
import Data.List.Split (unfoldrchunksOf)
 
-- LEONARDO NUMBERS -------------------------------------- LEONARDO NUMBERS ---------------------
-- L0 -> L1 -> Add number -> Series (infinite)
leo :: Integer -> Integer -> Integer -> [Integer]
Line 292 ⟶ 1,284:
fibonacci = leo 0 1 0
 
-- TEST -------------------------------------------- TEST ---------------------------
main :: IO ()
main = do
let twoLines = unlines . fmap (('\t' :) . show) . chunksOf 16
(putStrLn . unlines)
[ "First 25 default (1, 1, 1) Leonardo numbers:\n"
, twoLinesf $ take 25 leonardo
, "First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci numbers):\n"
, twoLinesf $ take 25 fibonacci
]</lang>
where
f = unlines . fmap (('\t' :) . intercalate ",") . chunksOf 16 . fmap show</syntaxhighlight>
{{Out}}
<pre>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]</pre>
 
Alternately, defining the list self-referentially instead of using unfoldr:
<syntaxhighlight lang="haskell">leo :: Integer -> Integer -> Integer -> [Integer]
leo l0 l1 d = s where
s = l0 : l1 : zipWith (\x y -> x + y + d) s (tail s)</syntaxhighlight>
 
=={{header|J}}==
<syntaxhighlight lang="j">
leo =: (] , {.@[ + _2&{@] + {:@])^:(_2&+@{:@[)
</syntaxhighlight>
{{Out}}
<pre>
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
</pre>
 
=={{header|Java}}==
{{trans|Kotlin}}
<syntaxhighlight lang="java">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));
}
}</syntaxhighlight>
{{out}}
<pre>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]</pre>
 
=={{header|JavaScript}}==
===ES6===
<syntaxhighlight lang="javascript">const leoNum = (c, l0 = 1, l1 = 1, add = 1) =>
new Array(c).fill(add).reduce(
(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));</syntaxhighlight>
 
<pre>
[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]</pre>
 
 
Or, taking N terms from a non-finite Javascript generator:
{{Trans|Python}}
<syntaxhighlight lang="javascript">(() => {
'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();
})();</syntaxhighlight>
{{Out}}
<pre>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</pre>
 
=={{header|jq}}==
===Naive Implementation===
<langsyntaxhighlight lang="jq">def Leonardo(zero; one; incr):
def leo:
if . == 0 then zero
Line 321 ⟶ 1,487:
else ((.-1) |leo) + ((.-2) | leo) + incr
end;
leo;</langsyntaxhighlight>
===Implementation with Caching===
An array is used for caching, with `.[n]` storing the value L(n).
<langsyntaxhighlight lang="jq">def Leonardo(zero; one; incr):
def leo(n):
if .[n] then .
Line 330 ⟶ 1,496:
| .[n] = .[n-1] + .[n-2] + incr
end;
. as $n | [zero,one] | leo($n) | .[$n];</langsyntaxhighlight>
 
(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.)
Line 336 ⟶ 1,502:
'''Examples'''
 
<langsyntaxhighlight lang="jq">[range(0;25) | Leonardo(1;1;1)]</langsyntaxhighlight>
{{out}}
<pre>[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]</pre>
 
<langsyntaxhighlight lang="jq">[range(0;25) | Leonardo(0;1;0)]</langsyntaxhighlight>
{{out}}
<pre>[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]</pre>
 
=={{header|Julia}}==
{{works with|Julia|0.6}}
 
<syntaxhighlight lang="julia">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
 
# Task 1
println("First 25 Leonardo numbers: ", join(L(0:24), ", "))
 
# Task 2
@show L(0) L(1)
 
# Task 4
println("First 25 Leonardo numbers starting with [0, 1]: ", join(L(0:24, 0, [0, 1]), ", "))</syntaxhighlight>
 
{{out}}
<pre>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</pre>
 
=={{header|Kotlin}}==
<langsyntaxhighlight lang="scala">// version 1.1.2
 
fun leonardo(n: Int, l0: Int = 1, l1: Int = 1, add: Int = 1): IntArray {
Line 360 ⟶ 1,554:
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(" "))
}</langsyntaxhighlight>
 
{{out}}
Line 372 ⟶ 1,566:
 
=={{header|Lua}}==
<langsyntaxhighlight lang="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}
Line 391 ⟶ 1,585:
 
show("Leonardo numbers", leoNums(25))
show("Fibonacci numbers", leoNums(25, 0, 1, 0))</langsyntaxhighlight>
{{out}}
<pre>Leonardo numbers:
Line 399 ⟶ 1,593:
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</pre>
 
=={{header|Perl 6Maple}}==
 
<syntaxhighlight lang="maple">L := proc(n, L_0, L_1, add)
<lang perl6>sub 𝑳 ( $𝑳0 = 1, $𝑳1 = 1, $𝑳add = 1 ) { $𝑳0, $𝑳1, { $^n2 + $^n1 + $𝑳add } ... * }
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)])
# Part 1
say "The first 25 Leonardo numbers:";
put 𝑳()[^25];
 
Fibonacci := n -> (L(0, 1, 0), [seq(0..n - 1)])</syntaxhighlight>
# Part 2
<pre>[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]
say "\nThe 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]</pre>
put 𝑳( 0, 1, 0 )[^25];</lang>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">L[0,L0_:1,___]:=L0
L[1,L0_:1,L1_:1,___]:=L1
L[n_,L0_:1,L1_:1,add_:1]:=L[n-1,L0,L1,add]+L[n-2,L0,L1,add]+add
 
L/@(Range[25]-1)
L[#,0,1,0]&/@(Range[25]-1)</syntaxhighlight>
 
<pre>{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}</pre>
 
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
/* Function that return the terms of an specified Leonardo sequence */
leo_specified(n,L0,L1,add):=block(
if n=0 then L[n]:L0 else if n=1 then L[n]:L1 else L[n]:L[n-1]+L[n-2]+add,
L[n])$
 
/* Test cases */
/* First 25 terms of Leonardo numbers (specification (1,1,1)) */
makelist(leo_specified(i,1,1,1),i,0,25);
 
/* First 25 terms of Fibonacci numbers (specification (0,1,0)) */
makelist(leo_specified(i,0,1,0),i,0,25);
</syntaxhighlight>
{{out}}
<pre>
<pre>The first 25 Leonardo numbers:
[1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973,3193,5167,8361,13529,21891,35421,57313,92735,150049,242785]
 
[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]
</pre>
 
 
=={{header|min}}==
{{works with|min|0.19.3}}
<syntaxhighlight lang="min">(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</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Modula-2}}==
The first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:
<syntaxhighlight lang="modula2">MODULE Leonardo;
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</pre>
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
 
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);
 
ReadChar
END Leonardo.</syntaxhighlight>
 
=={{header|Nim}}==
<syntaxhighlight lang="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)</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|OCaml}}==
<syntaxhighlight lang="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]</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Perl}}==
<syntaxhighlight lang="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";</syntaxhighlight>
{{out}}
<pre>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
</pre>
 
=={{header|Odin}}==
<syntaxhighlight lang="Go">
package main
/* imports */
import "core:fmt"
/* main */
main :: proc() {
fmt.println("\nThe first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
result := leonardo(25, 1, 1, 1)
fmt.println(result)
delete(result)
fmt.println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
result = leonardo(25, 0, 1, 0)
fmt.println(result)
delete(result)
}
/* definitions */
leonardo :: proc(n, l0, l1, add: int) -> []int {
leo := make([]int, n)
leo[0] = l0
leo[1] = l1
for i in 2 ..< n {
leo[i] = leo[i - 1] + leo[i - 2] + add
}
return leo
}
</syntaxhighlight>
{{out}}
<pre>
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]
</pre>
 
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">leonardo</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l1</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l2</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- return the first n leonardo numbers, starting {l1,l2}, with step as the add number</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">l1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l2</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[$]+</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?{</span><span style="color: #008000;">"Leonardo"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">leonardo</span><span style="color: #0000FF;">(</span><span style="color: #000000;">25</span><span style="color: #0000FF;">)}</span>
<span style="color: #0000FF;">?{</span><span style="color: #008000;">"Fibonacci"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">leonardo</span><span style="color: #0000FF;">(</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)}</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{"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}}
</pre>
 
=={{header|Picat}}==
<syntaxhighlight lang="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
leonardo(I1,_I2,_Add,0) = I1.
leonardo(_I1,I2,_Add,1) = I2.
leonardo(I1,I2,Add,N) = leonardo(I1,I2,Add,N-1) + leonardo(I1,I2,Add,N-2) + Add.</syntaxhighlight>
 
{{out}}
<pre>[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]</pre>
 
 
=={{header|PicoLisp}}==
<syntaxhighlight lang="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))</syntaxhighlight>
{{out}}
<pre>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)</pre>
 
=={{header|Plain English}}==
<syntaxhighlight lang="plainenglish">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.</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|PureBasic}}==
<syntaxhighlight lang="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
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Python}}==
===Finite iteration===
<syntaxhighlight lang="python">def Leonardo(L_Zero, L_One, Add, Amount):
terms = [L_Zero,L_One]
while len(terms) < Amount:
new = terms[-1] + terms[-2]
new += Add
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
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
===Non-finite generation===
Or, for a non-finite stream of Leonardos, we can use a Python generator:
{{Works with|Python|3}}
<syntaxhighlight lang="python">'''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()</syntaxhighlight>
{{Out}}
<pre>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]</pre>
 
=={{header|Quackery}}==
 
<syntaxhighlight lang="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 ]</syntaxhighlight>
 
{{out}}
 
<pre>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
</pre>
 
 
=={{header|R}}==
<syntaxhighlight lang="rsplus">
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")
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Racket}}==
<langsyntaxhighlight lang="racket">#lang racket
(define (Leonardo n #:L0 (L0 1) #:L1 (L1 1) #:1+ (1+ 1))
(cond [(= n 0) L0]
Line 436 ⟶ 2,127:
(check-equal? (Leonardo 1) 1)
(check-equal? (Leonardo 2) 3)
(check-equal? (Leonardo 3) 5))</langsyntaxhighlight>
 
{{out}}
<pre>'(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)</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
 
<syntaxhighlight lang="raku" line>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];</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|REXX}}==
<langsyntaxhighlight lang="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.*/
Line 467 ⟶ 2,177:
$=$ 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. */</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
Line 487 ⟶ 2,197:
=={{header|Ring}}==
 
<syntaxhighlight lang="ring">
{{incomplete|Rino| <br><br> The 2<sup>nd</sup> part of the output isn't complete. <br> The Fibonacci series computed with the 3<sup>rd</sup> equation for the Leonardo series isn't shown. <br><br>}}
# Project : Leanardo numbers
 
<lang ring>
# Project : Leonardo numbers
# Date : 2017/09/21
# Author : Gal Zsolt (~ CalmoSoft ~)
# Email : <calmosoft@gmail.com>
 
n0 = 1
n1 = 1
add = 1
see ""First +25 n0 + "Leonardo numbers:" + n1nl
leonardo()
for i=3 to 25
n0 = 1
temp=n1
n1 = 1
n1=n0+n1+add
add = 0
n0=temp
see "First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):" + nl
see " "+ n1
see "" + add + " "
next
leonardo()
</lang>
 
func leonardo()
see "" + n0 + " " + n1
for i=3 to 25
temp=n1
n1=n0+n1+add
n0=temp
see " "+ n1
next
see nl
</syntaxhighlight>
Output:
<pre>
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
</pre>
 
=={{header|RPL}}==
{{works with|Halcyon Calc|4.2.7}}
{| class="wikitable"
! Code
! Comments
|-
|
≪ → l0 l1 add n
≪ l0 l1 2 →LIST
'''IF''' n 3 ≥
'''THEN'''
l0 l1 2 n 1 - '''START'''
DUP ROT + add +
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
|}
{{in}}
<pre>
1 1 1 25 '''LENDO'''
0 1 0 25 '''LENDO'''
</pre>
{{out}}
<pre>
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 }
</pre>
===One-liner===
≪ 3 MAX → l0 l1 add n ≪ l0 l1 2 n '''START''' DUP2 + add + '''NEXT''' n 1 + →LIST ≫ ≫ ''''LEONE'''' STO
{{in}}
<pre>
1,1,1,24 '''LEONE'''
0,1,0,24 '''LEONE'''
</pre>
Same output as above.
 
=={{header|Ruby}}==
Enumerators are nice for this.
<syntaxhighlight lang="ruby">def leonardo(l0=1, l1=1, add=1)
return to_enum(__method__,l0,l1,add) unless block_given?
loop do
yield l0
l0, l1 = l1, l0+l1+add
end
end
 
p leonardo.take(25)
p leonardo(0,1,0).take(25)
</syntaxhighlight>
{{out}}
<pre>[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]
</pre>
 
=={{header|Run BASIC}}==
<syntaxhighlight lang="runbasic">sqliteconnect #mem, ":memory:"
#mem execute("CREATE TABLE lno (name,L0,L1,ad)")
#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$()
L0 = #row L0()
L1 = #row L1()
ad = #row ad()
print :print name$;" add=";ad :print" ";L0;" ";L1;" ";
for i = 3 to 25
temp = L1
L1 = L0 + L1 + ad
L0 = temp
print L1;" ";
next i
next j
end</syntaxhighlight>
<pre>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
Fibonacci 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
</pre>
 
=={{header|Rust}}==
<syntaxhighlight lang="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;
n1 += n + add;
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!();
}</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|Scala}}==
<langsyntaxhighlight lang="scala">def leo( n:Int, n1:Int=1, n2:Int=1, addnum:Int=1 ) : BigInt = n match {
case 0 => n1
case 1 => n2
Line 525 ⟶ 2,367:
(0 until 25) foreach { n => print( leo(n, n1=0, n2=1, addnum=0) + " " ) }
}
</syntaxhighlight>
</lang>
{{out}}
<pre>The first 25 Leonardo Numbers:
Line 532 ⟶ 2,374:
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
</pre>
 
=={{header|Seed7}}==
<syntaxhighlight lang="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;</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|Sidef}}==
<langsyntaxhighlight lang="ruby">func 𝑳(n, 𝑳0 = 1, 𝑳1 = 1, 𝑳add = 1) {
{ (𝑳0, 𝑳1) = (𝑳1, 𝑳0 + 𝑳1 + 𝑳add) } * n
return 𝑳0
Line 544 ⟶ 2,416:
 
say "\nThe first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:"
say 25.of { 𝑳(_, 0, 1, 0) }</langsyntaxhighlight>
{{out}}
<pre>
Line 552 ⟶ 2,424:
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]
</pre>
 
=={{header|Swift}}==
<syntaxhighlight lang="swift">struct Leonardo: Sequence, IteratorProtocol {
private let add : Int
private var n0: Int
private var n1: Int
init(n0: Int = 1, n1: Int = 1, add: Int = 1) {
self.n0 = n0
self.n1 = n1
self.add = add
}
mutating func next() -> Int? {
let n = n0
n0 = n1
n1 += n + add
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: " "))</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|VBA}}==
 
<syntaxhighlight lang="vb">
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
</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<syntaxhighlight lang="vbnet">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</syntaxhighlight>
{{out}}
<pre>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</pre>
 
=={{header|V (Vlang)}}==
{{trans|go}}
<syntaxhighlight lang="v (vlang)">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))
}</syntaxhighlight>
 
{{out}}
<pre>
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]
</pre>
 
=={{header|Wren}}==
<syntaxhighlight lang="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()</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|Yabasic}}==
<syntaxhighlight lang="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</syntaxhighlight>
 
 
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">int N, L, L0, L1, Add;
[Text(0, "Enter L(0), L(1), Add: ");
L0:= IntIn(0);
L1:= IntIn(0);
Add:= 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;
];
]</syntaxhighlight>
 
{{out}}
<pre>
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
</pre>
 
=={{header|zkl}}==
<langsyntaxhighlight lang="zkl">fcn leonardoNumber(n, n1=1,n2=1,addnum=1){
if(n==0) return(n1);
if(n==1) return(n2);
self.fcn(n-1,n1,n2,addnum) + self.fcn(n-2,n1,n2,addnum) + addnum
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">println("The first 25 Leonardo Numbers:");
foreach n in (25){ print(leonardoNumber(n)," ") }
println("\n");
Line 566 ⟶ 2,641:
println("The first 25 Fibonacci Numbers:");
foreach n in (25){ print(leonardoNumber(n, 0,1,0)," ") }
println();</langsyntaxhighlight>
{{out}}
<pre>
Line 573 ⟶ 2,648:
 
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
</pre>
 
=={{header|Python}}==
<lang python>def Leonardo(L_Zero, L_One, Add, Amount):
terms = [L_Zero,L_One]
while len(terms) < Amount:
new = terms[-1] + terms[-2]
new += Add
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
</lang>
{{out}}
<pre>
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
</pre>
PureFox
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