Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences

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Can Kızılateş
Wei-Shih Du
Feng Qi


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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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.


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