Fibonacci

The nth Fibonacci number, with and , extended to negative n by the same recurrence.

WikipediaFibonacci sequenceFibonacci numberMathWorldFibonacciNumberWikidataQ47577Britannicatopic/Fibonacci-numberDLMF26.11.p4FungrimFibonacci✓Fungrim entryOEISA000045Wolfram LanguageFibonacci✓Rosetta CodeFibonacci sequence

Fibonacci(n)the nth Fibonacci number .

SageMathfibonacci(n)SymPyfibonacci(n)

Domain: Sequences

Details

Defined by the recurrence with , .
Closed form (Binet's formula): , where and .
Consecutive ratios converge to the golden ratio . See LucasL.
GCD identity: .
Extends to negative n via .
compute-engine only accepts a single integer index (no threading over a list, no complex ).

Examples

See also: LucasL