Abstract

In this paper we deal with some properties of the solutions of the recursive sequence $$x_{n+1}=ax_{n-1}+\frac{bx_{n-1}x_{n-3}}{cx_{n-1}+dx_{n-3}},\quad n=0,1,\ldots,$$ where the initial conditions x −3, x −2, x −1, x 0 are arbitrary positive real numbers and a, b, c, d are constants. Also, we give the form of the solution of some special cases of this equation.

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