Recurrence Relation for Sequence of mth Powers of Fibonacci Numbers/Examples/m = 3

Example of Recurrence Relation for Sequence of mth Powers of Fibonacci Numbers

 * ${F_n}^n - 2 {F_{n + 1} }^2 - 2 {F_{n + 2} }^2 + {F_{n + 3} }^2 = 0$

Proof
Set $m = 3$ into Recurrence Relation for Sequence of mth Powers of Fibonacci Numbers:


 * $\ds \sum_{k \mathop \in \Z} \dbinom m k_\FF \paren {-1}^{\ceiling {\paren {m - k} / 2} } {F_{n + k} }^{m - 1} = 0$