Definition:Second Order Fibonacci Number

Definition
The second order Fibonacci numbers are a sequence $\left \langle {\mathcal F_n}\right \rangle$ of integers which is formally defined recursively for all $n \in \Z_{\ge 0}$ as:


 * $\mathcal F_n = \begin{cases} 0 & : n = 0 \\

1 & : n = 1 \\ \mathcal F_{n - 1} + \mathcal F_{n - 2} + F_{n - 2} & : \text{otherwise} \end{cases}$

where $F_{n - 2}$ denotes the $n - 2$th Fibonacci number.