On the Horadam sequence of order three

Authors

  • S. Amrouche University of Science and Technology Houari Boumediene, P.B. 32, El Alia, 16111 Bab Ezzouar, Algeria
  • H. Belbachir University of Science and Technology Houari Boumediene, P.B. 32, El Alia, 16111 Bab Ezzouar, Algeria
  • C. Cesarano International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy https://orcid.org/0000-0002-1694-7907
  • P.E. Ricci International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy https://orcid.org/0000-0002-7899-3087
https://doi.org/10.15330/cmp.17.2.406-415

Keywords:

Horadam sequence, $q$-analogue, recurrence relation
Published online: 2025-07-22

Abstract

In this paper, we define a generalized Horadam triangle in which the sum of elements located along the diagonal lines corresponds to the terms of generalized Horadam sequence of order three. We establish a relation between generalized Horadam triangle and the generalized Delannoy triangle. Additionally, we define the $q$-analogue of the generalized Tribonacci sequence and generalized Horadam sequence of order three.

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How to Cite
(1)
Amrouche, S.; Belbachir, H.; Cesarano, C.; Ricci, P. On the Horadam Sequence of Order Three. Carpathian Math. Publ. 2025, 17, 406-415.