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

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.

## closed as off-topic by user223391, Leucippus, Shailesh, Namaste, Alex MathersDec 25 '16 at 0:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Leucippus, Shailesh, Namaste, Alex Mathers
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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.)