TWO ASPECTS OF A GENERALIZED FIBONACCI SEQUENCE - Tuwankotta, Johan Matheus (IndoMS, 2015)
In this paper we study the so-called generalized Fibonacci sequence: x_n+2 = α x_n+1 + β x_n, nN. We derive an open domain around the origin of the parameter space where the sequence converges to 0. The limiting behavior on the boundary of this domain are: convergence to a nontrivial limit, k-periodic (kN), or quasi-periodic. We use the ratio of two consecutive terms of the sequence to construct a rational approximation for algebraic numbers of the form: r, rQ. Using a similar idea, we extend this to higher dimension to construct a rational approximation for [3] a + bc + [3] a - bc + d.DOI : http://dx.doi.org/10.22342/jims.21.1.173.1-17