Generalızed pell sequences related to the extended generalızed hecke groups (H)over-bar(3,q) and an applıcatıon to the group (h)over-bar(3,3)

Abstract

We consider the extended generalized Hecke groups (H) over bar (3,q) generated by X (z) = -(z - 1)(-1), Y (z) = -(z + lambda(q))(-1) with lambda(q) = 2 cos(pi/q) where q >= 3 an integer. In this work, we study the generalized Pell sequences in (H) over bar (3,q). Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group (H) over bar (3,3) can be written by using Pell, Pell-Lucas and modified-Pell numbers.