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On Third-Order $\overline{h}$-Jacobsthal and Third-Order $\overline{h}$-Jacobsthal--Lucas Sequences, and Related Quaternions

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Submitted:

19 April 2020

Posted:

19 April 2020

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Abstract
In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.
Keywords: 
recurrence relations; quaternions; third-order Jacobsthal numbers; third-order Jacobsthal--Lucas numbers
Subject: 
Computer Science and Mathematics  -   Algebra and Number Theory
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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