# A Combinatorial Problem Solved by a Meta-Fibonacci Recurrence Relation

## TL;DR

This paper introduces a simple combinatorial problem whose solution is described by a specific meta-Fibonacci recurrence relation involving a prime number, expanding understanding of such relations in combinatorics.

## Contribution

It presents a new, simpler combinatorial problem linked to a meta-Fibonacci recurrence, providing clearer insight compared to more general previous problems.

## Key findings

- Solution characterized by a prime-based meta-Fibonacci recurrence
- Simpler combinatorial problem with clear relation to the recurrence
- Advances understanding of recurrence relations in combinatorics

## Abstract

We present a natural, combinatorial problem whose solution is given by the meta-Fibonacci recurrence relation $a(n) = \sum_{i=1}^p a(n-i+1 - a(n-i))$, where $p$ is prime. This combinatorial problem is less general than those given in [3] (B. Jackson, F. Ruskey, 2006) and [4] (F. Ruskey, C. Deugau, 2009), but it has the advantage of having a simpler statement.