Prove tight worst-case asymptotic upper bounds for the following recurrence equation that depends on a variable q \in [0, n/4]. Note that you need to prove an upper bound that is true for every value of q \in [0, n/4] and a matching lower bound for a specific value of q \in [0, n/4] of your choosing. Do not assume that a specific q yields the worst case input; instead, formally identify the q which maximizes the running time.

Note, it should be a MATH proof, not a copy/pasted c++ program.

T(n) = 1 if n<= 2

T(n) = T(n-2q-1) + T(3q/2) + T(q/2) +Theta(1) otherwise