2022/04/08 by Bartosz Sobolewski, Sobolewski, Bartosz, Maciej Ulas +1
Physics and Astronomy · Computer Science · Mathematics · #Advanced Mathematical Theories and Applications #semigroups and automata theory #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2204.04011
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≤ 1, we prove that the resulting integer sequence is closely related to the function counting binary partitions of a certain type.