Partial sums of Horadam sequences: sum-free representations via generating functions

TL;DR

This paper derives simple generating function-based formulas for partial sums of Horadam sequences, providing efficient and elegant representations for these sums.

Contribution

It introduces straightforward generating function methods to compute partial sums of Horadam sequences, simplifying previous approaches.

Findings

Generated simple formulas for partial sums

Provided efficient computational methods

Enhanced understanding of Horadam sequence properties

Abstract

Horadam sequences and their partial sums are computed via generating functions. The results are as simple as possible.