Definition:Fibonacci Number

Definition
The Fibonacci numbers are a sequence $\left \langle {F_n}\right \rangle$ of integers which is formally defined recursively as:


 * $F_n = \begin{cases} 0 & : n = 0 \\

1 & : n = 1 \\ F_n = F_{n - 1} + F_{n - 2} & : \text{otherwise} \end{cases}$

for all $n \in \Z_{\ge 0}$. That is, the next integer in the sequence is found by adding together the two previous ones.

Also known as
According to some sources, this sequence is also known as Lamé's Sequence, after. However, this suggestion is difficult to corroborate.

Also see

 * Definition:General Fibonacci Sequence
 * Definition:Lucas Number