A Note on Third-order $k-$Jacobsthal and Third-order $k-$Jacobsthal–Lucas Sequences, and Related Quaternions

Year 2025, Volume: 17 Issue: 2, 310 - 321, 30.12.2025

Gamaliel Morales

https://doi.org/10.47000/tjmcs.1529324

Abstract

In this paper, inspired by recent articles of Anatriello and Vincenzi and Morales , we will introduce the third-order $k$-Jacobsthal and third-order $k$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in [12].

Keywords

Recurrence relation , quaternion , third-order Jacobsthal number , third-order Jacobsthal--Lucas number.

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