Section 4.4 of "Introduction to Algorithms, 3rd Edition By Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein" illustrates how a recursion tree provides a good guess for the recurrence
$$T(n) = 3T(\lfloor n/4 \rfloor) + \Theta(n^2) = 3T(n/4) + cn^2$$
where c is a constant.
The authors assume that n is an exact power of 4.
I agree with the tolerable sloppiness and understand the basic idea of that section.
I'd just like to know about some other trivial details.
For convenience, assume T(1)=1, so $T(4)=3T(4/4)+c4^2=3T(1)+c4^2$, what about T(2) and T(3)?
Does it make sense to yield $T(2)=T(1)+c2^2$?