Definition:Second Order Fibonacci Number
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Definition
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.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers: Exercise $12$