Unimodality and linear recurrences associated with rays in the Delannoy triangle

Abstract

In this paper, we study the unimodality of sequences located in the infinite transversals of the Delannoytriangle. We establish recurrence relations associated with the sum of elements laying along the finite transversals of thecited triangle and we give the generating function of the established sum. Moreover, new identities for the odd and eventerms of the Tribonacci sequence are given. Finally, we define a q -analogue for the Delannoy numbers and we proposea q -deformation of the Tribonacci sequence.