the fibonacci-circulant sequences in the binary polyhedral groups

In 2017 deveci et al. defined the fibonacci-circulant sequences of the first and second kinds as shown, respectively: x^ 1 n = −x^ 1 n−1 + x^ 1 n−2 − x^ 1 n−3 for n ≥ 4, where x^ 1 1 = x^ 1 2 = 0 and x^ 1 3 = 1 and x^ 2 n = −x^ 2 n−3 − x^ 2 n−4 + x^ 2 n−5 for n ≥ 6, where x^ 2 1 = x^ 2 2 = x^ 2 3 = x^ 2 4 = 0 and x^ 2 5 = 1. also, they ex^tended the fibonacci-circulant sequences of the first and second kinds to groups. in this paper, we obtain the periods of the fibonacci-circulant sequences of the first and second kinds in the binary polyhedral groups.