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.

The notation for the $n$th Fibonacci number is not universally standardised.

In much professional literature, $u_n$ is used.

$F_n$ tends to appear more in amateur publications, but $F_n$ is rapidly taking over as standard.

$F_n$ is the notation used in.

Also see

 * Definition:General Fibonacci Sequence
 * Definition:Lucas Number
 * Definition:Golden Mean