-nacci sequences in some special groups of finite order

In this paper, we obtain the period of k -nacci sequences in the semidihedral groups S D 2 m and in the ordinary nonabelian group having the presentations W 2 m = 〈 a , b : a 2 m − 1 = b 2 = 1 , a b = a 1 + 2 m − 2 〉 of order 2 m , m ≥ 4 . It is important to note that the Fibonacci length depends on the chosen generating n -tuple for a group.