Solutions of certain meta-Fibonacci recurrences
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≤ 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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