`fibonacci`

Fibonacci numbers.

Syntax

F = fibonacci(n)

Returns the n-th Fibonacci number, with F_0 = 0 and F_1 = 1.

Description

Each Fibonacci number is the sum of the two before it: F_n = F_(n-1) + F_(n-2). The ratio of consecutive terms tends to the golden ratio. Doubles hold the numbers exactly only up to about F_78, after which they are rounded.

For large indices use a symbolic argument: fibonacci(sym(100)) returns the exact 21-digit integer.

Input arguments

n: Integer scalar or array. Use sym(n) for exact values of large indices.

Output arguments

F: Fibonacci numbers: doubles for numeric input, exact integers for symbolic input.

Example

First terms and an exact large one

fibonacci(0:10)
fibonacci(sym(100))

Output

ans = 1×11

     0     1     1     2     3     5     8    13    21    34    55
ans = 354224848179261915075

Notes

Negative indices are not handled like MATLAB, which follows F(-n) = (-1)^(n+1)*F(n); MatLivre returns 0. The two-argument polynomial form is not supported either.

fibonacci