On Linear Recursive Sequences with Coefficients in Arithmetic-Geometric Progressions

TL;DR

This paper generalizes recent results on linear recurrence relations with coefficients in progressions, exploring their connections to well-known integer sequences and offering multiple solution approaches, concluding with an open problem.

Contribution

It introduces a broader class of linear recurrence relations with coefficients in arithmetic-geometric progressions and provides new methods for solving them.

Findings

Connections to Fibonacci, Pell, Jacobsthal, and Balancing sequences

Multiple approaches to solving the recurrence relations

Open problem proposed for future research

Abstract

We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci sequence, Pell sequence, Jacobsthal sequence, and the Balancing sequence of numbers. The paper also provides several approaches in solving the linear recurrence relation under consideration. We end the paper by giving out an open problem.