On the adjacency-pell numbers

Abstract

In this paper, we define the adjacency-Pell sequences and then we obtain their miscellaneous properties such as the generating matrix, the Binet formula, the permanental representations, the de-terminantal representations, the combinatorial representations, the generating function, the exponential representation and the sums. Also, we obtain the cyclic groups by the generating matrices of the adjacency-Pell numbers when read modulo a and we study the adjacency-Pell sequences modulo a. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the adjacency-Pell sequences modulo a. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.