I am trying to find a closed form of the following recurrence relation. $a_n, b_n, s_n, X_0$ are given for all $n$.
\begin{equation} X_{n+1} = a_n(1 - s_n^2) + s_n^2\frac{X_n + b_n}{2} + s_n\frac{|X_n - b_n|}{2} \end{equation}
If there is no closed form, how could I approach a proof?