The recurrence $a_n = 6a_{n-1} - 9a_{n-2}$ has characteristic equation $(r-3)^2 = 0$, yielding a repeated root $r = 3$. The general solution is $a_n = (c_1 + c_2 n) \cdot 3^n$. Given $a_0 = 2$ and $a_1 = 9$, compute $a_3$.