f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n-3) for n >= 3

Find the formula for f(n) and prove it using mathmatical induction.

I found f(n) to be:

{ 0 if n=1(mod3)

{ 2^[cieling(n/3)] otherise

I am confused how to prove this using induction