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http://dx.doi.org/10.5831/HMJ.2019.41.1.197

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 (Institute of Sciences, Department of Mathematics, Balikesir University)
Koruoglu, Ozden (Necatibey Faculty of Education, Department of Mathematics, Balikesir University)
Sahin, Recep (Faculty of Arts and Sciences, Department of Mathematics, Balikesir University)
Demir, Bilal (Necatibey Faculty of Education, Department of Mathematics, Balikesir University)
Publication Information
Honam Mathematical Journal / v.41, no.1, 2019 , pp. 197-206 More about this Journal
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;
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