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:


 * $\displaystyle \sum_{k \mathop \in \Z} \dbinom m k_\mathcal F \left({-1}\right)^{\left\lceil{\left({m - k}\right) / 2}\right\rceil} {F_{n + k} }^{m - 1} = 0$