On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

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 rela...

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Autores principales:	Bajorska-Harapińska Beata, Ludew Jakub Jan, Smoleń-Duda Barbara, Wituła Roman
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	split quaternions quaternions quasi-fibonacci numbers quaternaccis split quaternaccis 11b83 11e88 11r52 11b37 11b39 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7115f07f5e0346a7bb70cd148a2a8538
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id	oai:doaj.org-article:7115f07f5e0346a7bb70cd148a2a8538
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spelling	oai:doaj.org-article:7115f07f5e0346a7bb70cd148a2a85382021-12-05T14:10:53ZOn split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis2391-545510.1515/math-2021-0059https://doaj.org/article/7115f07f5e0346a7bb70cd148a2a85382021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0059https://doaj.org/toc/2391-5455In 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.Bajorska-Harapińska BeataLudew Jakub JanSmoleń-Duda BarbaraWituła RomanDe Gruyterarticlesplit quaternionsquaternionsquasi-fibonacci numbersquaternaccissplit quaternaccis11b8311e8811r5211b3711b39MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 583-599 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	split quaternions quaternions quasi-fibonacci numbers quaternaccis split quaternaccis 11b83 11e88 11r52 11b37 11b39 Mathematics QA1-939
spellingShingle	split quaternions quaternions quasi-fibonacci numbers quaternaccis split quaternaccis 11b83 11e88 11r52 11b37 11b39 Mathematics QA1-939 Bajorska-Harapińska Beata Ludew Jakub Jan Smoleń-Duda Barbara Wituła Roman On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
description	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.
format	article
author	Bajorska-Harapińska Beata Ludew Jakub Jan Smoleń-Duda Barbara Wituła Roman
author_facet	Bajorska-Harapińska Beata Ludew Jakub Jan Smoleń-Duda Barbara Wituła Roman
author_sort	Bajorska-Harapińska Beata
title	On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
title_short	On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
title_full	On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
title_fullStr	On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
title_full_unstemmed	On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
title_sort	on split quaternion equivalents for quaternaccis, shortly split quaternaccis
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/7115f07f5e0346a7bb70cd148a2a8538
work_keys_str_mv	AT bajorskaharapinskabeata onsplitquaternionequivalentsforquaternaccisshortlysplitquaternaccis AT ludewjakubjan onsplitquaternionequivalentsforquaternaccisshortlysplitquaternaccis AT smolendudabarbara onsplitquaternionequivalentsforquaternaccisshortlysplitquaternaccis AT witułaroman onsplitquaternionequivalentsforquaternaccisshortlysplitquaternaccis
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On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

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