On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

Bajorska-Harapińska Beata; Ludew Jakub Jan; Smoleń-Duda Barbara; Wituła Roman

doi:10.1515/math-2021-0059

Open Mathematics (Jul 2021)

On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

Bajorska-Harapińska Beata,
Ludew Jakub Jan,
Smoleń-Duda Barbara,
Wituła Roman

Affiliations

Bajorska-Harapińska Beata: Department of Mathematics, Silesian Univesity of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Ludew Jakub Jan: Department of Mathematics, Silesian Univesity of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Smoleń-Duda Barbara: Department of Mathematics, Silesian Univesity of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Wituła Roman: Department of Mathematics, Silesian Univesity of Technology, Kaszubska 23, 44-100 Gliwice, Poland

DOI: https://doi.org/10.1515/math-2021-0059
Journal volume & issue: Vol. 19, no. 1
pp. 583 – 599

Abstract

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In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras. Explicit and recurrent formulae for Split Quaternacci sequences are given, as well as generating functions. Also, matrices related to Split Quaternaccis sequences are investigated. Moreover, new identities connecting Horadam sequences with other known sequences are generated. Analogous identities for Horadam quaternions and split Horadam quaternions are proved.

Published in Open Mathematics

ISSN: 2391-5455 (Online)
Publisher: De Gruyter
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://www.degruyter.com/journal/key/math/html

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