On the Horadam sequence of order three - Amrouche, S.; Belbachir, H.; Cesarano, C.; Ricci, P.E. (Carpathian Mathematical Publications, 2025)
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.