d-Tribonacci Polynomials and Their Matrix Representations

Abstract

In this study, we define d-Tribonacci polynomials. Some combinatorial properties of the d- Tribonacci polynomials with matrix representations are obtained with the help of Riordan arrays. In addition, d- Tribonacci number sequence, which is a new generalization of this number sequence, has been obtained by considering Pascal matrix. With the help of Pascal matrix, two kinds of factors of d-Tribonacci polynomials were found. Also, infinite d-Tribonacci polynomials matrix and the inverses of these polynomials were found.