Asked this before, but could not seem to get an answer. As such, I've simplified my question a bit.
We have the following recurrence $T$: $$ T(n,k) = \left\{ \begin{array}{ll} \alpha n^2 + \beta n + \delta & \quad \text{if }\; n \le k \\ T(\lceil n / 2 \rceil, k) + T(\lfloor n / 2 \rfloor, k) + \gamma n + \zeta & \quad \text{if }\; n > k \\ \end{array} \right. $$
for all positive integers $n$ and $k$
I want to find a closed-form of $T$. The closest I have is:
$$\gamma n\text{log }_2(n)+2n - \zeta$$
but is not correct as it does not work for all positive integers $n$.
I am really confused on how to get a closed form or summation for $T$.