Generalized pell sequences in some principal congruence subgroups of the hecke groups

Abstract

In this paper, we consider the Hecke groups H(root m) for m = 1, 2 and 3. Firstly, we give the generators of the principal congruence subgroups H-2(root m) of H(root m), respectively. Then, using some of these generators, we define a sequence U-k which is generalized version of the Pell numbers sequence P-k given in [12] for the modular group, in the extended Hecke groups H(root m) for m = 1, 2 and 3.