Unrestricted Tribonacci and Tribonacci–Lucas quaternions

Gonca Kızılaslan and Leyla Karabulut
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 310–321
DOI: 10.7546/nntdm.2023.29.2.310-321
Full paper (PDF, 287 Kb)

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Authors and affiliations

Gonca Kızılaslan
Department of Mathematics, Faculty of Science and Arts,
Kırıkkale University, TR-71450 Kırıkkale, Turkey

Leyla Karabulut
Department of Mathematics, Graduate School of Natural and Applied Sciences,
Kırıkkale University, TR-71450 Kırıkkale, Turkey

Abstract

We define a generalization of Tribonacci and Tribonacci–Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci–Lucas numbers coefficients, respectively. We get generating functions and Binet’s formulas for these quaternions. Furthermore, several sum formulas and a matrix representation are obtained.

Keywords

• Quaternion
• Recurrences
• Integer sequences

2020 Mathematics Subject Classification

• 11R52
• 11B37
• 11Y55

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Manuscript history

• Received: 15 June 2022
• Revised: 19 February 2023
• Accepted: 2 May 2023
• Online First: 8 May 2023

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Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).