On the third-order Horadam matrix sequences

Abstract

In this paper, we first give new generalizations for third-order Horadam $\{H_n^{(3)}{\}}_{n\in \mathbb{N}}$ and generalized Tribonacci $\{h_n^{(3)}{\}}_{n\in \mathbb{N}}$ sequences for classic Horadam and generalized Fibonacci numbers. Considering these sequences, we define the matrix sequences which have elements of $\{H_n^{(3)}{\}}_{n\in \mathbb{N}}$ and $\{h_n^{(3)}{\}}_{n\in \mathbb{N}}$. Then we investigate their properties.

11 pages. arXiv admin note: text overlap with arXiv:1806.03709, arXiv:1812.11617