Trees and Meta-Fibonacci Sequences
Trees and Meta-Fibonacci Sequences
For $k>1$ and nonnegative integer parameters $a_p, b_p$, $p = 1..k$, we analyze the solutions to the meta-Fibonacci recursion $C(n)=\sum_{p=1}^k C(n-a_p-C(n-b_p))$, where the parameters $a_p, b_p$, $p = 1..k$ satisfy a specific constraint. For $k=2$ we present compelling empirical evidence that solutions exist only for two particular families of parameters; …