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Several determinantal expressions of generalized Tribonacci polynomials and sequences
  • Can Kizilates,
  • Wei-Shih Du,
  • Feng Qi
Can Kizilates
Zonguldak Bulent Ecevit University
Wei-Shih Du
National Kaohsiung Normal University
Feng Qi
Henan Polytechnic University, Inner Mongolia University for Nationalities, Tianjin Polytechnic University
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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.