We use the Lie group analysis method to investigate the invariance properties and the solutions of \begin{ align*} x_{ n+1} =\frac{ x_{ n-5}x_{ n-3}}{ x_{ n-1}(a_n +b_nx_{ n-5}x_{ n-3})}. \end{ align*} We show that this equation has a two-dimensional Lie algebra and that its solutions can be presented in a unified manner. Besides presenting solutions of the recursive sequence above where $(a_n)$ and $(b_n)$ are sequences of real numbers, some specific cases are emphasized.
Categories: math.DS