On the Difference Equation x n + 1 = x n x n − 2 − 1

Abstract

The long-term behavior of solutions of the following difference equation: $x_{n+1}=x_n{x}_{n-2}-1$, $n\in {\mathbb{N}}_0$, where the initial values $x_{-2}$, $x_{-1}$, $x_0$ are real numbers, is investigated in the paper.