Integer sequence and perfect squares II

Let the integer sequence $(x_n)$ be defined by $x_1 = x_2 = 1$ and $$x_{n+2} = 3x_{n+1} + 2x_n, \quad \forall n \in \mathbb{N}^*.$$ Find the sum of all positive integers $n$ such that $17x_n^2 - (-2)^{n+2}$ is a perfect square.