Definition:General Fibonacci Sequence

Definition
Let $r$ and $s$ be numbers, usually integers but not necessarily so limited.

Let $\left\langle{a_n}\right\rangle$ be the sequence defined as:
 * $a_n = \begin{cases}

r & : n = 0 \\ s & : n = 1 \\ a_{n - 2} + a_{n - 1} & : n > 1 \end{cases}$

Then $\left\langle{a_n}\right\rangle$ is a general Fibonacci sequence.

Also see

 * Definition:Fibonacci Numbers: the general Fibonacci sequence where $r = s = 1$
 * Definition:Lucas Numbers: the general Fibonacci sequence where $r = 2, s = 1$