ON THE ADJACENCY-PELL NUMBERS

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 determinantal 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 alpha and we study the adjacency-Pell sequences modulo alpha. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the adjacency-Pell sequences modulo alpha.