Generalized fibonacci sequences related to the extended hecke groups and an application to the extended modular group

Abstract

The extended Hecke groups H(λq) are generated by T(z) = -1/z, S(z) = -1/(z +λq) and R(z) = 1/z with λq = 2cos(π/q) for q ≥ 3 integer. In this paper, we obtain a sequence which is a generalized version of the Fibonacci sequence given in [6] for the extended modular group Γ, in the extended Hecke groups H(λq). Then we apply our results to Γ to find all elements of the extended modular group Γ. © TÜBİTAK.