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 cyclicfibonacci 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 d2, d3, d4, d5, d6 and d8 with respect to their generating sets.