# Tetranacci and Tetranacci-Lucas Quaternions

## TL;DR

This paper introduces Tetranacci and Tetranacci-Lucas quaternions, exploring their properties and relationships within the algebraic structure of quaternions, expanding the mathematical understanding of these special sequences.

## Contribution

The paper presents the first definition and analysis of Tetranacci and Tetranacci-Lucas quaternions, including their properties and interrelations.

## Key findings

- Defined Tetranacci and Tetranacci-Lucas quaternions
- Derived properties and identities of these quaternions
- Established relationships between Tetranacci and Tetranacci-Lucas quaternions

## Abstract

The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them.