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Solutions of certain meta-Fibonacci recurrences

Bartosz Sobolewski, Maciej Ulas Acta Arithmetica MSC: Primary 11B37; Secondary 11B39, 11B83, 11B85. DOI: 10.4064/aa220613-19-1 Opublikowany online: 6 March 2023

Streszczenie

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.

Autorzy

  • Bartosz SobolewskiInstitute of Mathematics
    Faculty of Mathematics and Computer Science
    Jagiellonian University
    30-348 Kraków, Poland
    e-mail
  • Maciej UlasInstitute of Mathematics
    Faculty of Mathematics and Computer Science
    Jagiellonian University
    30-348 Kraków, Poland
    e-mail

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