MathNet 2012 Question 74

A real number sequence $a_1, a_2, \dots, a_n, \dots$ is such that $a_1 = 1$, $a_2 = 9$ and $a_{n+2} = 14a_{n+1} - a_n - 4$ for all positive integers $n$. Prove that for each positive integer $n$ the number $a_n$ is a square of integer.