# Fibonacci: Fibonacci Numbers

Description Usage Arguments Details Value Author(s) References Examples

### Description

Generates Fibonacci numbers.

### Usage

 `1` ```Fibonacci(n) ```

### Arguments

 `n` nonnegative integer or vector of nonnegative integers.

### Details

Generates the `n`-th Fibonacci number, whereas Fibonacci(0) = 0.

### Value

A single integer, or a vector of integers.

### Author(s)

Andri Signorell <andri@signorell.net>

### References

http://en.wikipedia.org/wiki/Fibonacci_number

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```Fibonacci(0) # 1 Fibonacci(2) # 2 Fibonacci(0:3) # 0 1 1 2 # Golden ratio F <- Fibonacci(1:25) # ... 75025 121393 f25 <- F[25]/F[24] # 1.618033989 phi <- (sqrt(5) + 1)/2 abs(f25 - phi) # 7.945178e-11 # Fibonacci numbers without iteration fibo <- function(n) { phi <- (sqrt(5) + 1)/2 fib <- (phi^(n+1) - (1-phi)^(n+1)) / (2*phi - 1) round(fib) } fibo(30:33) # 1346269 2178309 3524578 5702887 ```

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