Solutions of certain meta-Fibonacci recurrences

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. In the case 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 (independently of the value of $f(2)\in\mathbb{N}$).

The talk is based on a joint work with Bartosz Sobolewski.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)