Birol, Furkan; Koruoğlu, Özden; Sahin, Recep; Demir, Bilal Generalized Pell sequences related to the extended generalized Hecke groups \({\overline{H}}_{3,q}\) and an application to the group \({\overline{H}}_{3,3}\). (English) Zbl 1423.20059 Honam Math. J. 41, No. 1, 197-206 (2019). Summary: We consider the extended generalized Hecke groups \({\overline{H}}_{3,q}\) 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 \({\overline{H}}_{3,q}\). Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group \({\overline{H}}_{3,3}\) can be written by using Pell, Pell-Lucas and modified-Pell numbers. 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