The quaternion-type cyclic-balancing sequence in groups

OpenAlex İngilizce

In this research, several types of definitions of the quaternion-type cyclic-balancing sequence are presented. The Cassini formula and generating function of these sequences are also obtained for all types. The quaternion-type cyclic-balancing sequences modulo m, the first step to transferring this topic to group theory, are examined. These sequences in finite groups are then defined. Eventually, the lengths of periods for these sequences of the generalized quaternion group are calculated.