SMO 2016 Senior Round 1 Question 30

A sequence $a_1,a_2,a_3,\ldots$ satisfies $$a_{n+3}=2 a_{n+2}-2 a_{n+1}+a_n$$ for n=1,2,3,... . If $a_1=11$, $a_2=222$ and $a_3=7777$, find $a_{2016}$.