Elimination by Multiplication - Examples & Practice

The sequence $a_0$, $a_1$, $a_2$, $\ldots$ satisfies the recurrence equation $$a_n = 2 a_{n-1} - 2 a_{n - 2} + a_{n - 3}$$ for every integer $n \ge 3$. If $a_{20} = 1$, $a_{25} = 10$, and $a_{30} = 100$, what is the value of $a_{1331}$?

Source: Math Prize for Girls