I am solving the recurrence relation: $$ T(n) = n + \sum_{i=1}^{\lfloor \log_3 n \rfloor} T(\lfloor \frac {n}{3^i} \rfloor), $$
It looks that T(n) at every level is being divided by 3 and the depth of this tree is: $$ \lfloor \log_3 n \rfloor $$ Also, expanding first few terms, I got :
$$ T(1) = 1 1$$
$$ T(2) = 2 + T(1) = 3$$
$$ T(3) = 3 + T(1) = 4$$
I have to find a tight asymptotic bound for this recurrence. I am confused about how to proceed from here. Thanks for any help.