The Fibonacci-Circulant Sequences in the Binary Polyhedral Groups

Abstract

Deveci et al. defined 6. 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 x₁¹=x₂¹=0 and x₃¹=1and x_{n}²=-x_{n-3}²-x_{n-4}²+x_{n-5}² for n≥6, where x₁²=x₂²=x₃²=x₄²=0 and x₅²=1.Also, they extended the Fibonacci-circulant sequences of the first and second kinds to groups. In this work, we obtain the periods of the Fibonacci-circulant sequences of the first and second kinds in the binary polyhedral groups.