Some identities of generalized Tribonacci and Jacobsthal polynomials

Abdeldjabar Hamdi and Salim Badidja
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 137—147
DOI: 10.7546/nntdm.2021.27.2.137-147
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Authors and affiliations

Abdeldjabar Hamdi
Faculty of Mathematics, University of Youcef Benkhedda Algiers 01
02 Rue Didouche Mourad, 16 000 Algeria

Salim Badidja ​
Faculty of Mathematics, University of Kasdi Merbah
Ouargla Route de Ghardaia, BP. 511, 30 000 Algeria


In this study, we denote (t'_{n}(x))_{n\in \mathbb{N}} the generalized Tribonacci polynomials, which are defined by t'_{n}(x)=x^{2}t'_{n-1}(x)+xt'_{n-2}(x)+t'_{n-3}(x), n \geqslant 4, with t_{1}(x)=a, t_{2}(x)=b, t_{3}(x)=cx^{2} and we drive an explicit formula of (t'_{n}(x))_{n\in \mathbb{N}} in terms of their coefficients T'(n,j), Also, we establish some properties of (t_{n}(x))_{n\in \mathbb{N}}. Similarly, we study the Jacobsthal polynomials (J_{n}(x))_{n\in \mathbb{N}}, where J_{n}(x)=J_{n-1}(x)+x J_{n-2}(x)+ x^{2} J_{n-3}(x), n \geqslant 4, with J_{1}(x)= J_{2}(x)=1, J_{3}(x)=x+1 and describe some properties.


  • Tribonacci polynomials
  • Generalized Tribonacci polynomials
  • Jacobsthal polynomials

2020 Mathematics Subject Classification

  • 11B39
  • 11B83


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Cite this paper

Hamdi, A., & Badidja, S. (2021). Some identities of generalized Tribonacci and Jacobsthal polynomials. Notes on Number Theory and Discrete Mathematics, 27(2), 137-147, doi: 10.7546/nntdm.2021.27.2.137-147.

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