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_n^1 = -x_(n-1)^1+x_(n-2)^1-x_(n-3)^1 for n≥4,where x_1^1=x_2^1=0 and x_3^1=1 and x_n^2 = -x_(n-3)^2-x_(n-4)^2+x_(n-5)^2 for n≥6,where x_1^2=x_2^2=x_3^2=x_4^2=0 and x_5^2=1 Also, they extended 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. Keywords