VN-TST 2012 Problem 4

Consider the sequence $(x_n)_{n\ge 1}$ where $x_1=1,x_2=2011$ and $x_{n+2}=4022x_{n+1}-x_n$ for all $n\in\mathbb{N}$ . Prove that $\frac{x_{2012}+1}{2012}$ is a perfect square.