Solving Third Order Linear Difference Equations in Terms of Second Order Equations

TL;DR

This paper introduces algorithms for absolute factorization of difference operators and demonstrates how to solve third order difference equations using second order equations, with applications to OEIS sequences.

Contribution

It presents novel algorithms for absolute factorization and solving third order difference equations in terms of second order equations, expanding computational methods in difference equations.

Findings

Algorithms for absolute factorization of difference operators.

Method to solve third order difference equations via second order equations.

Applications demonstrated on OEIS sequences.

Abstract

We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in terms of second order equations, together with applications to OEIS sequences. The latter algorithm is similar to existing algorithms for differential equations.