On the previous midterm, there was a question that I couldn't solve. It gave us this sequence
The sequence $$a_0, a_1, a_2,... $$is defined by $$a_0 = 1,$$ and for all integers $$n > 0,$$ $$a_n = a_{\lfloor n/2 \rfloor} + a_{\lfloor 2n/3 \rfloor} + n. $$
Prove by Strong Induction that $a_n >4n$ for all integers $n>a$. where a is the integer you chose in part (b).
I got to the part where I figured out that the lowest integer that could be used was 3, but I didn't know how to prove by strong induction, as I had forgotten the difference between regular induction and strong induction.
Would 3 be the basis of our proof? If so? What would the inductive step look like?