Article ID: MTJPAM-D-20-00013

Title: Generating Functions of Generalized Tribonacci and Tricobsthal Polynomials

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00013; Volume 2 / Issue 2 / Year 2020, Pages 7-37

Document Type: Research Paper

Author(s): Hind Merzouk a , Ali Boussayoud b , Mourad Chelgham c

aMohamed Seddik Ben Yahia University, LMAM Laboratory and Department of Mathematics, Jijel, Algeria

bMohamed Seddik Ben Yahia University, LMAM Laboratory and Department of Mathematics, Jijel, Algeria

cMohamed Seddik Ben Yahia University, LMAM Laboratory and Department of Mathematics, Jijel, Algeria

Received: 12 May 2020, Accepted: 4 September 2020, Available online: 23 September 2020.

Corresponding Author: Ali Boussayoud (Email address:

Full Text: PDF


In this paper, we introduce a symmetric endomorphism operator δa1a2k allows us to obtain a new generating functions involving the product of generalized Tribonacci and Tricobsthal polynomials with k-Mersenne numbers.

Keywords: Symmetric functions, Generating functions, Generalized Tricobsthal Polynomials, Generalized Tribonacci polynomials

  1. A. Boussayoud and S. Boughaba, On Some Identities and Generating Functions for k-Pell sequences and Chebyshev polynomials, Online J. Anal. Comb. 14, 1-13, 2019.
  2. A. Boussayoud, S.Boughaba, M. Kerada, S. Araci and M.Acikgoz, Symmetric Functions of Binary Products of k-Fibonacci and Orthogonal Polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM. 113 , 2575-2586, 2019.
  3. A. Boussayoud, On some identities and generating functions for Pell-Lucas numbers, Online.J. Anal. Comb. 12 (1), 1-10, 2017.
  4. A. Boussayoud, M.kerada and M. Boulyer, A simple and accurate method for determination of some generalized sequence of numbers, Int.J.Pure Appl Math. 108, 503-511, 2016.
  5. A. Boussayoud, M. Bolyer and M. Kerada, On Some Identities and Symmetric Functions for Lucas and Pell numbers, Electron. J. Math. Analysis Appl. 5, 202-207, 2017.
  6. Kh. Boubellouta, A. Boussayoud and M. Kerada, Symmetric Functions for Second-Order Recurrence Sequences, Tbil. Math. J. 13, 225-237, 2020.
  7. S. Boughaba, A. Boussayoud and M. Kerada, Construction of Symmetric Functions of Generalized Fibonacci Numbers, Tamap J.Mathematics and Statistics 3, 1–7, 2019.
  8. M. Elia, Derived sequences, the Tribonacci recurrence and cubic forms, Fibonacci Q. 39, 107-109, 2001.
  9. M. Feinberg, Fibonacci-Tribonacci, Fibonacci Q. 1, 70-74, 1963.
  10. Jr. V.E. Hoggatt and M. Bicknell, Generalized Fibonacci polynomials, Fibonacci Q. 11, 457-465, 1973.
  11. E. Kilic, Tribonacci sequences with certain indices and their sums, Ars Comb. 86, 13-22, 2008.
  12. T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publication, 2001.
  13. V.E. Hoggatt and M. Bicknell, Generalized fibonacci polynomials, Fibonacci Q. 11 (5), 457–465, 1973.
  14. B. Rybołowicz and A. Tereszkiewicz, Generalized Tricobsthal and generalized Tribonacci polynomials, Appl. Math. Comput. 325, 297-305, 2018.
  15. N. Yilmaz and N. Taskara, Tribonacci and Tribonacci-Lucas numbers via the determinants of special matrices, Appl. Math. Sci. 8, 1947-1955, 2014.
  16. J.S. Ramirez and V.F. Sirvent, Incomplete Tribonacci Numbers and Polynomials, J. Integer Seq. 17, 1-13, 2014.
  17. A. Tereszkiewicz and I. Wawreniuk, Generalized Jacobsthal polynomials and special points for them, Appl. Math. Comput. 268, 806–814, 2015.
  18. K. Uslo and V. Denis, Somme identities of k-Mersenne numbers, Adv. Appl. Discrete Math. 18, 413-423, 2017.