The complex-type cyclic-Fibonacci sequence and its applications

In the present paper, we aim to generalize the notion of complex-type Fibonacci sequences to complex-type cyclic Fibonacci sequences. Firstly, we define the complex-type cyclic-Fibonacci sequence and then we give miscellaneous  properties of this sequence by using the matrix method. Also, we study the complex-type cyclic-Fibonacci sequence modulo m. In addition, we describe the complex-type cyclic-Fibonacci sequence in a 2-generator group and investigate that in finite groups in details. Then, as our last result, we obtain the lengths of the periods of the complex-type cyclic-Fibonacci sequences in dihedral groups D_{2}, D_{3}, D_{4}, D_{5}, D_{6} and D_{8} with respect to their generating sets.

کلیدواژه های The complex-type cyclic-Fibonacci sequence and its applications:

The complex-type cyclic-Fibonacci sequence ، Matrix ، Group ، Period