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Information Journal Paper

Title

The complex-type cyclic-Fibonacci sequence and its applications

Pages

  235-246

Abstract

 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.

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