Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences

Authors

  • 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

DOI:

https://doi.org/10.5556/j.tkjm.53.2022.3743

Keywords:

Generalized Tribonacci sequence, Tribonacci polynomial, Tribonacci number, Hessenberg determinant

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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Published

2022-08-01

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

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Papers