Using tools of the theory of orthogonal polynomials we obtain the generating function of the generalized Fibonacci sequence established by Petronilho for a sequence of real or complex numbers {Qn}1 n=0 defined by Q0 = 0, Q1 = 1, Qm = ajQm1 + bjQm2, m j (mod k), where k 3 is a fixed integer, and a0, a1, . . . , ak1, b0, b1, . . . , bk1 are 2k given real or complex numbers, with bj 6= 0 for 0 ? j ? k 1. For this sequence some convergence proprieties are obtained.
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