Fibonacci numbers along residue classes and convolutions

TL;DR

This paper explores Fibonacci numbers within residue classes and their convolutions, extending previous work to more general cases involving Chebyshev polynomials, providing deeper insights into their mathematical properties.

Contribution

It generalizes the study of Fibonacci sequences in residue classes to include arbitrary shifts using Chebyshev polynomials, advancing theoretical understanding.

Findings

Extended Fibonacci residue class analysis to general h values

Connected Fibonacci convolutions with Chebyshev polynomials

Provided new formulas and properties for these sequences

Abstract

The sequence $F_{dn+h}$ and its convolutions have (for $h=0$) been studied in a recent paper at the arxiv [arXiv:2603.08636]. The instance with general $h$ is more involved and uses Chebyshev polynomials.