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arXiv · 2204.04011

Solutions of certain meta-Fibonacci recurrences

Bartosz Sobolewski·Maciej Ulas
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Abstract

In this note 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.

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Bartosz Sobolewski, Maciej Ulas. 2022-04-08. Solutions of certain meta-Fibonacci recurrences. https://arxiv.org/abs/2204.04011

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