Explicit solution of system of two higher-order recurrences

TL;DR

This paper presents a method for explicitly solving systems of two higher-order linear recurrence relations, with applications demonstrated through a domino tiling problem.

Contribution

The paper introduces an efficient method for solving inhomogeneous systems of two higher-order recurrences, illustrated with a combinatorial tiling problem.

Findings

Method successfully finds explicit solutions to complex recurrence systems.

Application to domino tiling demonstrates practical utility.

Provides a new tool for combinatorial problem solving.

Abstract

We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by considering a tiling problem with black and white dominoes, and we use the method as a demonstration to find the solution.