Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 19 April 2020 / Approved: 19 April 2020 / Online: 19 April 2020 (12:36:16 CEST)

How to cite: Cerda-Morales, G. On Third-Order $\overline{h}$-Jacobsthal and Third-Order $\overline{h}$-Jacobsthal--Lucas Sequences, and Related Quaternions. Preprints 2020, 2020040343 (doi: 10.20944/preprints202004.0343.v1). Cerda-Morales, G. On Third-Order $\overline{h}$-Jacobsthal and Third-Order $\overline{h}$-Jacobsthal--Lucas Sequences, and Related Quaternions. Preprints 2020, 2020040343 (doi: 10.20944/preprints202004.0343.v1).

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}.

Subject Areas

recurrence relations; quaternions; third-order Jacobsthal numbers; third-order Jacobsthal--Lucas numbers

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