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
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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).
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Cite this paper
Kızılaslan, G., & Karabulut, L. (2023). Unrestricted Tribonacci and Tribonacci–Lucas quaternions. Notes on Number Theory and Discrete Mathematics, 29(2), 310-321, DOI: 10.7546/nntdm.2023.29.2.310-321.