# GENERALIZED PELL SEQUENCES RELATED TO THE EXTENDED GENERALIZED HECKE GROUPS ${\bar{H}}$3,q AND AN APPLICATION TO THE GROUP ${\bar{H}}$3,3

Birol, Furkan;Koruoglu, Ozden;Sahin, Recep;Demir, Bilal

• Accepted : 2018.10.29
• Published : 2019.03.25
• 16 2

#### Abstract

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

#### Keywords

Extended generalized Hecke groups;Generalized Pell sequence;Pell-Lucas numbers;modified-Pell numbers