Fibonacci

Returns the nth Fibonacci number.

Syntax

• Fibonacci(n)

  • n is a non-negative integer

Description

If n is a non-negative integer, then Fibonacci(n) is the nth Fibonacci number. The Fibonacci numbers F(n) are defined recursively by

       ⎧ 1                      if n = 0
F(n) = ⎨ 1                      if n = 1
       ⎩ F(n − 1) + F(n − 2)    otherwise.

Examples

SequenceVector(20) @ Fibonacci

(1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765)

filter(SequenceVector(50) @ Fibonacci, IsPrime)

(2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073)

∑(1/Fibonacci(n), n, 1, 100)

3.35988566624

∑(1/(1 + Fibonacci(2⋅n + 1)), n, 0, 100)

1.11803398875	(=√5/2)

See also

• Lucas