BALTIC-WAY 2011 Problem 16

Let $a$ be any integer. Define the sequence $x_0,x_1,\ldots$ by $x_0=a$ , $x_1=3$ , and for all $n>1$ $$x_n=2x_{n-1}-4x_{n-2}+3.$$ Determine the largest integer $k_a$ for which there exists a prime $p$ such that $p^{k_a}$ divides $x_{2011}-1$ .