The Complex-type Cyclic-Pell Sequence and its Applications

Abstract

In this paper, we define the complex-type cyclic-Pell sequence and then, we give miscellaneous properties of this sequence by using matrix method. Also, we study the complex-type cyclic-Pell sequence modulo m. In addition, we describe the complex-type cyclic-Pell sequence in a 2-generator group and we investigate that in finite groups in detail. Finally, we obtain the lengths of the periods of the complex-type cyclic-Pell sequences in dihedral groups D2, D3, D4, D6, D8, D16 and D32 with respect to the generating pair (x, y).