# Golf a Custom Fibonacci Sequence

The Fibonacci sequence is a fairly well known thing around here. Heck, it even has its own tag. However, for all that, we sure like to stick to our roots of 1, 1, ... (or is it 0, 1, ...? We may never know...). In this challenge, the rules are the same, but instead of getting the nth item in the Fibonacci sequence, you will get the nth item in the Fibonacci-esque sequence starting with x, y, ....

# Input

Three integers, in whatever order you want. n is the index (0 or 1 indexed) of term in the sequence for your output. x and y are the first two items in your current program run's Fibonacci sequence.

# Output

The nth term in the Fibonacci sequence starting with x, y.

# Test Cases

(0-indexed)

n   x     y     out
5   0     0     0
6   0     1     8
6   1     1     13
2   5     5     10
10  2     2     178
3   3     10    23
13  2308  4261  1325165
0   0     1     0
1   0     1     1


(1-indexed)

n   x     y     out
6   0     0     0
7   0     1     8
7   1     1     13
3   5     5     10
11  2     2     178
4   3     10    23
14  2308  4261  1325165
1   0     1     0
2   0     1     1


# Caveats

Assume 0 <= x <= y.

• Can we take a list as input? – Business Cat May 17 '17 at 14:41
• @BusinessCat you mean like [1, 2, 3]? Yes. Whatever you need to accept 3 integers. – Stephen May 17 '17 at 14:42
• @StephenS How about taking an input as n,[x,y] where n is a number and x and y are numbers in a list? That's probably being a little too flexible though ;) – Tom May 17 '17 at 14:54
• Related – xnor May 17 '17 at 22:55

# Jelly, 3 bytes

+¡ạ


Takes x, y, and n (0-indexed) as separate command-line arguments, in that order.

Try it online!

### How it works

+¡ạ  Main link. Left argument: x. Right argument: y. Third argument: n

ạ  Yield abs(x - y) = y - x, the (-1)-th value of the Lucas sequence.
+¡   Add the quicklink's left and right argument (initially x and y-x), replacing
the right argument with the left one and the left argument with the result.
Do this n times and return the final value of the left argument.


# CJam, 14 9 bytes

l~{_@+}*;


Try it online!

Input format is "x y n". I'm still a noob at this, so I'm 100% sure there are better ways to do this, but please instead of telling me "do this" try to only give me hints so that I can find the answer myself and get better. Thanks!

• ririri can be shortened to 2 bytes. fI can be shortened to 1 byte. – Dennis May 17 '17 at 14:54
• Welcome to PPCG! – Martin Ender May 17 '17 at 14:54
• @Dennis improved! Thank you! And thanks for the welcome. – FrodCube May 17 '17 at 15:04

# Python 2, 37 bytes

f=lambda x,y,n:n and f(y,x+y,n-1)or x


Try it online!

0-indexed, you may need to adjust the recursion limit for n≥999

# JavaScript (ES6), 27 26 bytes

Nothing fancy here, just a standard JS Fibonacci function with the initial values of 0 & 1 removed.

n=>g=(x,y)=>n--?g(y,x+y):x


## Try it

f=
n=>g=(x,y)=>n--?g(y,x+y):x
o.value=f(i.value=13)(j.value=2308,k.value=4261)
oninput=_=>o.value=f(+i.value)(+j.value,+k.value)
*{font-family:sans-serif;}
input{margin:0 5px 0 0;width:50px;}
#o{width:75px;}
<label for=i>n: </label><input id=i type=number><label for=j>x: </label><input id=j type=number><label for=k>y: </label><input id=k type=number><label for=o>= </label><input id=o>

## Python 2, 40 bytes

0-indexed
Try it online

n,a,b=input()
exec'a,b=b,a+b;'*n
print a

• Haha not subject to a recursion/stack limit unlike some other answers. Nice trick. – ShreevatsaR May 19 '17 at 4:16
• @ShreevatsaR Thanks! But recursive lambda beats me anyway :D – Dead Possum May 19 '17 at 8:17

x#y=(f!!)where f=x:scanl(+)y f


Try it online! 0-indexed. Use as (x#y)n, e.g. (0#1)5 for the fifth element of the original sequence.

The most likely shortest way to get the Fibonacci sequence in Haskell is f=0:scanl(+)1f, which defines an infinite list f=[0,1,1,2,3,5,8,...] containing the sequence. Replacing 0 and 1 with arguments x and y yields the custom sequence. (f!!) is then a function returning the nth element of f.

## Mathematica, 36 bytes

LinearRecurrence[{1,1},{##2},{#+1}]&


input

[n,x,y]

• You can use ##2 instead of #2,#3. – alephalpha May 18 '17 at 8:45
• very nice! fixed! – J42161217 May 18 '17 at 8:58

# PowerShell, 40 bytes

$n,$x,$y=$args;2..$n|%{$y=$x+($x=$y)};$y


Try it online!

# Brain-Flak, 38 bytes

{({}[()]<(({}<>)<>{}<(<>{}<>)>)>)}{}{}


Try it online!

{({}[()]<                      >)}     # For n .. 0
(({}<>)<>            )        # Copy TOS to the other stack and add it to...
{}                   # The second value
<(<>{}<>)>         # Copy what was TOS back
{}{} # Pop the counter and the n+1th result


# Ruby, 27 bytes

->a,b,n{n.times{b=a+a=b};a}


# Jelly, 6 bytes

;SḊµ¡I


Try it online!

Explanation

   µ¡  - repeat n times (computes the n+1th and n+2th element):
S     -  take the sum of the elements of the previous iteration (starting at (x,y))
;      -  append to the end of the previous iteration
Ḋ    -  remove the first element
I - Take the difference of the n+1th and n+2th to get the n-th.


# TAESGL, 4 bytes

ēB)Ė


1-indexed

Interpreter

Explanation

Input taken as n,[x,y]

 ēB)Ė
AēB)     get implicit input "A" Fibonacci numbers where "B" is [x,y]
Ė    pop the last item in the array


# Prolog (SWI), 77 bytes

f(N,Y,Z):-M is N-1,f(M,X,Y),Z is X+Y.
l(N,A,B,X):-asserta(f(0,A,B)),f(N,X,_).


Try it online!

Started off golfing Leaky Nun's answer and arrived at something completely different.

This one has a rule for (Nᵗʰ, (N+1)ᵗʰ) in terms of ((N-1)ᵗʰ, Nᵗʰ) and uses database management to assert 0ᵗʰ and 1ˢᵗ elements at runtime.

f(N,X,Y) means Nᵗʰ element is X and (N+1)ᵗʰ element is Y.

# Octave, 24 bytes

@(n,x)(x*[0,1;1,1]^n)(1)


Input format: n,[x,y].

Try it online!

# Braingolf, 15 bytes

VR<2-M[R!+v]R_;


_; is no longer needed on the latest version of Braingolf, however that's as of ~5 minutes ago, so would be non-competing.

# Python 2, 112 bytes

1-indexed.

import itertools
def f(x,y):
while 1:yield x;x,y=y,x+y
def g(x,y,n):return next(itertools.islice(f(x,y),n-1,n))


Try it online!

• Erp, too late and too big. – totallyhuman May 17 '17 at 14:12

# MATL, 7 bytes

:"wy+]x


Output is 0-based.

Try it at MATL Online!

### Explanation

Let the inputs be denoted n (index), a, b (initial terms).

:"     % Implicitly input n. Do this n times
%   At this point in each iteration, the stack contains the two most
%   recently computed terms of the sequence, say s, t. In the first
%   iteration the stack is empty, but a, b will be implicitly input
%   by the next statement
w    %   Swap. The stack contains t, s
y    %   Duplicate from below. The stack contains t, s, t
+    %   Add. The stack contains t, s+t. These are now the new two most
%   recently comnputed terms
]      % End
x      % Delete (we have computed one term too many). Implicitly display


# R, 39 bytes

f=function(x,y,n)'if'(n,f(y,x+y,n-1),x)


A simple recursive function. Funnily enough this is shorter than anything I can come up with for the regular Fibonacci sequence (without built-ins), because this doesn't have to assign 1 to both x and y =P

Calculates n+1 numbers of the sequence, including the initial values. Each recursion is calculates with n-1 and stopped when n==0. The lowest of the two numbers is then returned, giving back the n-th value.

# dc, 36 bytes

?sdsbsa[lddlb+sdsbla1-dsa1<c]dscxldp


Try it online!

0-indexed. Input must be in the format n x y.

# Common Lisp, 49 Bytes, 0-indexed

(defun fib(n x y)(if(= 0 n)x(fib(1- n)y(+ x y))))


I'm a Lisp noob so any tips would be appreciated ;)

### Explanation:

(defun fib(n x y)                                  | Define a function taking 3 arguments
(if(= 0 n)x                       | If n = 0, return x
(fib(1- n)y(+ x y))))  | Otherwise, call fib with n-1, y, and x+y


# Prolog (SWI), 85 bytes

l(0,X,Y,X).
l(1,X,Y,Y).
l(N,X,Y,C):-M is N-1,P is N-2,l(M,X,Y,A),l(P,X,Y,B),C is A+B.


Try it online!

0-indexed.

• Could you edit this answer? I seem to have accidentally downvoted it the day you posted it. – Esolanging Fruit Apr 21 '18 at 22:29
• @EsolangingFruit done – Leaky Nun Apr 21 '18 at 22:30

# br**nfuck, 39 29 bytes

Thanks to @JoKing for -10!

,<,<,[>[>+>+<<-]<[>+<-]>-]>>.


TIO won't work particularly well for this (or for any BF solution to a problem involving numbers). I strongly suggest @Timwi's EsotericIDE (or implementing BF yourself).

Takes x, then y, then n. 0-indexed. Assumes an unbounded or wrapping tape.

### Explanation

,<,<,            Take inputs. Tape: [n, y, x]
[                While n:
> [->+>+<<]      Add y to x, copying it to the next cell along as well. Tape: [n, 0, x+y, y]
< [>+<-]         Move n over. Tape: [0, n, x+y, y]
>-               Decrement n.
] >>.            End loop. Print cell 2 to the right (x for n == 0).

• Why do you bother moving x and y when you can just move n? Try It Online – Jo King Apr 21 '18 at 23:07
• @JoKing Considered that (but longer on my own), but it doesn't quite work, unless OP allows "-1-indexing". – Khuldraeseth na'Barya Apr 21 '18 at 23:35
• Oh, just add a > to the end or swap x and y order – Jo King Apr 21 '18 at 23:48
• @JoKing My palm hit my face quite hard just now. Thanks! – Khuldraeseth na'Barya Apr 21 '18 at 23:53
• Why did you bother to censor "brain" but not the second word in the programming language's name? – MilkyWay90 Mar 12 '19 at 16:51

# C (gcc), 29 bytes

f(n,x,y){n=n?f(n-1,y,x+y):x;}


Try it online!

This implementation is 0-based.

• Nice, and welcome! Here's a prettier TIO setup for testing, should you choose to use it. – Khuldraeseth na'Barya Apr 22 '18 at 0:19

# 05AB1E, 9 bytes

©GDŠ+}®@


Try it online!

Explanation

           # split inputs as separate to stack
©          # store n in register
G         # n-1 times do
D        # duplicate top of stack
Š       # move down 2 places on stack
+      # add top 2 values of stack
}     # end loop
®@   # get the value nth value from the bottom of stack


# Lua, 44 bytes

0-Indexed

n,x,y=...for i=1,n do
x,y=y,x+y
end
print(x)


Try it online!

# Klein, 18 + 3 bytes

This uses the 000 topology

:?\(:(+)$)1-+ ((/@  Pass input in the form x y n. # Axiom, 88 57 bytes f(k,x,y)==(repeat(k<=0=>break;c:=y;y:=x+y;x:=c;k:=k-1);x)  this would pass the test proposed (0 indexed) (14) -> f(5,0,0) (14) 0 Type: NonNegativeInteger (15) -> f(6,0,1) (15) 8 Type: PositiveInteger (16) -> f(2,5,5) (16) 10 Type: PositiveInteger (17) -> f(10,2,2) (17) 178 Type: PositiveInteger (18) -> f(3,3,10) (18) 23 Type: PositiveInteger (19) -> f(13,2308,4261) (19) 1325165 Type: PositiveInteger  # Retina, 37 bytes \d+$*1
+(1*) (1*) 1
$2$1\$2
.*

1


Try it online!

0-based, takes x y n separated by space. Calculates in unary.

# TI-Basic, 32 bytes

Prompt N,X,Y
While N
X+Y➡Z
Y➡X
Z➡Y
DS<(N,0
End
X
`