\begin{definition}[Definition:General Fibonacci Sequence]
Let $r, s, t, u$ be numbers, usually integers but not necessarily so limited.
Let $\sequence {a_n}$ be the sequence defined as:
:$a_n = \begin{cases}
r & : n = 0 \\
s & : n = 1 \\
t a_{n - 2} + u a_{n - 1} & : n > 1
\end{cases}$
Then $\sequence {a_n}$ is a '''general Fibonacci sequence'''.
\end{definition}