RosettaCodeData/Task/Fibonacci-sequence/00DESCRIPTION

The '''Fibonacci sequence''' is a sequence &nbsp; <big> F<sub>n</sub> </big> &nbsp;  of natural numbers defined recursively:

      <big><big> F<sub>0</sub> = 0 </big></big>
      <big><big> F<sub>1</sub> = 1 </big></big>
      <big><big> F<sub>n</sub> = F<sub>n-1</sub> + F<sub>n-2</sub>, if n>1 </big></big>


;Task:
Write a function to generate the &nbsp; <big> n<sup>th</sup> </big> &nbsp; Fibonacci number.

Solutions can be iterative or recursive (though recursive solutions are generally considered too slow and are mostly used as an exercise in recursion).

The sequence is sometimes extended into negative numbers by using a straightforward inverse of the positive definition:

      <big><big> F<sub>n</sub> = F<sub>n+2</sub> - F<sub>n+1</sub>, if n<0   </big></big>

support for negative &nbsp; &nbsp; <big> n </big> &nbsp; &nbsp; in the solution is optional.


;Related tasks:
* &nbsp; [[Fibonacci n-step number sequences‎]]
* &nbsp; [[Leonardo numbers]]


;References:
* &nbsp; [[wp:Fibonacci number|Wikipedia, Fibonacci number]]
* &nbsp; [[wp:Lucas number|Wikipedia, Lucas number]]
* &nbsp; [http://mathworld.wolfram.com/FibonacciNumber.html MathWorld, Fibonacci Number]
* &nbsp; [http://www.math-cs.ucmo.edu/~curtisc/articles/howardcooper/genfib4.pdf Some identities for r-Fibonacci numbers]
* &nbsp; [[oeis:A000045|OEIS Fibonacci numbers]]
* &nbsp; [[oeis:A000032|OEIS Lucas numbers]]
<br><br>