Given the equation
$$L_{n+k}-(-1)^kL_{n-k}=5F_kF_n$$
Where $\{L\}$ is the set of Lucas numbers and $\{F\}$ is a Fibonacci sequence, $n$ and $k$ are both $>0$ and integers, how would one develop this into a recursive relationship? Would a different approach be needed instead of just trying to rearrange my existing formula?