CN-LEAGUE 2000 Problem 2

Define the sequence $a_1, a_2, \ldots$ and $b_1, b_2, \ldots$ as $a_0=1,a_1=4,a_2=49$ and for $n \geq 0$ $$\begin{cases} a_{n+1}=7a_n+6b_n-3, b_{n+1}=8a_n+7b_n-4. \end{cases}$$ Prove that for any non-negative integer $n,$ $a_n$ is a perfect square.