ARS COMBINATORIA, cilt.120, ss.383-401, 2015 (SCI-Expanded)
In this paper, we study the generalized Pell p-sequences modulo M. Also, we define the generalized Pell p-sequences and the basic generalized Pell p-sequences in groups and then we examine these sequences in finite groups. Furthermore, we obtain the periods of the generalized Pell p-sequences and the basic periods of the basic generalized Pell p-sequences in the binary polyhedral groups < n,2,2 >, < 2,n,2 > and < 2,2,n >.