# On the third-order Horadam and geometric mean sequences

## TL;DR

This paper explores the properties of third-order Horadam and geometric mean sequences, establishing new connections with generalized Tribonacci numbers through independent proofs.

## Contribution

It introduces novel relationships between third-order Horadam sequences and geometric mean sequences, expanding understanding of their mathematical properties.

## Key findings

- New connections between third-order Horadam and generalized Tribonacci numbers
- Independent proofs establishing these relationships
- Enhanced understanding of geometric mean sequence properties

## Abstract

This paper, in considering aspects of the geometric mean sequence, offers new results connecting generalized Tribonacci and third-order Horadam numbers which are established and then proved independently.