On the Solutions of the Recursive Sequence $x_{n+1}=\frac{ax_{n-k}}{a-\prod\limits_{i=0}^{k}x_{n-i}}$

Saniye Ergin, Ramazan Karataş

Abstract

We obtain in thispaper the solutions of the difference equation\begin{equation*}x_{n+1}=\frac{ax_{n-k}}{a-\prod\limits_{i=0}^{k}x_{n-i}}\text{ \ for \ }%n=0,1,2,...\end{equation*} where $k$ is a positive number and initial conditions are non zeroreal numbers with $\prod_{i=0}^{k}x_{-i}\neq a$.