Solutions of certain meta-Fibonacci recurrences
Volume 209 / 2023
Acta Arithmetica 209 (2023), 269-289
MSC: Primary 11B37; Secondary 11B39, 11B83, 11B85.
DOI: 10.4064/aa220613-19-1
Published online: 6 March 2023
Abstract
We investigate the solutions of certain meta-Fibonacci recurrences of the form $f(n)=f(n-f(n-1))+f(n-2)$ for various sets of initial conditions. When $f(n)=1$ for $n\leq 1$, we prove that the resulting integer sequence is closely related to the function counting binary partitions of a certain type.
