\begin{definition}[Definition:Fibonacci Number/Negative]
The definition of '''Fibonacci numbers''' for negative integers is an extension of the definition for positive integers:
:$F_n = \begin{cases} 0 & : n = 0 \\
1 & : n = 1 \\
F_{n + 2} - F_{n + 1} & : n < 0 \end{cases}$
for all $n \in \Z$.
\end{definition}