Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences

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Published: Aug 1, 2022
DOI: https://doi.org/10.5556/j.tkjm.53.2022.3743
Keywords:
Generalized Tribonacci sequence, Tribonacci polynomial, Tribonacci number, Hessenberg determinant

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Can Kızılateş
Department of Mathematics, Faculty of Arts and Sciences, Zonguldak Bülent Ecevit University, Zonguldak, Turkey
Wei-Shih Du
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Feng Qi
https://orcid.org/0000-0001-6239-2968

Abstract

In the paper, the authors present several explicit formulas for the $(p,q,r)$-Tribonacci polynomials and generalized Tribonacci sequences in terms of the Hessenberg determinants and, consequently, derive several explicit formulas for the Tribonacci numbers and polynomials, the Tribonacci--Lucas numbers, the Perrin numbers, the Padovan (Cordonnier) numbers, the Van der Laan numbers, the Narayana numbers, the third order Jacobsthal numbers, and the third order Jacobsthal--Lucas numbers in terms of special Hessenberg determinants.

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How to Cite
Kızılateş, C., Du, W.-S., & Qi, F. (2022). Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences. Tamkang Journal of Mathematics, 53(3), 277–291. https://doi.org/10.5556/j.tkjm.53.2022.3743
Issue
Vol. 53 No. 3 (2022)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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