KöMaL 2008 B4129

Sequence ($a_n$) is defined by the recursion $a_0$=0, $a_1$=1 and $a_n$=2$a_{n-1}$+$a_{n-2}$ for $n$>1. Prove that if $2^k\mid n$ , then $2^k\mid a_n$.