\begin{definition}[Definition:Second Order Fibonacci Number]
The '''second order Fibonacci numbers''' are a sequence $\sequence {\FF_n}$ of integers which is formally defined recursively for all $n \in \Z_{\ge 0}$ as:
:$\FF_n = \begin{cases} 0 & : n = 0 \\
1 & : n = 1 \\
\FF_{n - 1} + \FF_{n - 2} + F_{n - 2} & : \text{otherwise} \end{cases}$
where $F_{n - 2}$ denotes the $n - 2$th Fibonacci number.
\end{definition}