VMO 1995 Problem 2

The sequence $a_0$, $a_1$, $a_2$, ... is defined by $a_0$ = 1, $a_1$ = 3, $a_{n+2}$ = $a_{n+1}$ + $9a_n$ for n even, $9a_{n+1}$ + $5a_n$ for n odd. Show that $a_{1995}^2$ + $a_{1996}^2$ + $a_{1997}^2$ + $a_{1998}^2$ + $a_{1999}^2$ + $a_{2000}^2$ is divisible by 20, and that no $a_{2n+1}$ is a square.