How to solve this recurrence relation? $a_n=(a_{n-1})^3\cdot a_{n-2}$

Question

I'm having some trouble solving this:

$a_n=(a_{n-1})^3\cdot a_{n-2}$

$a_0=1$

$a_1=3$

Thanks for any help

Edit:

Well all I could think of doing with this relation is finding several values and look for any pattern. I got powers of $3$ in the following order: $0, 1, 3, 10, 33, 109, 360, 1189, ... $

Couldn't find any pattern here.

Answer 1

Hint: Take logs of both sides and let $b_n=\ln a_n$. The resulting recurrence relation in $b_n$ is linear homogeneous. (To make it even simpler, take log base 3.)