MathNet 2014 Question 22

$x_0 = a$, $x_1 = 2$, $x_n = 2x_{n-1}x_{n-2} - x_{n-1} - x_{n-2} + 1$. Find all integers $a$ such that $2x_{3n}$ are perfect squares for $\forall n \in \mathbb{N}$.