How do we solve:
\begin{align} a_n &= 4a_{n-1} + 4a_{n-2}, \ \ \text{ for } n\ge 2\\ a_0 &= 6,\\ a_1 &= 8. \end{align}
I know we can solve it using characteristic equations i.e. considering $r^2 -4r + 4 = 0$ and then calculating the coefficients and all.
But is there a way to do it using generating functions?