This question: Solving the recurrence T(n) = 3T(n-2) with iterative method has a pretty straightforward step-by-step for solving this particular recurrence. But, I'm having trouble understanding two things.
1) How dos OP arrive at this general form? If we know
T(n−2)=3T(n−4), then my substitution gives:
Why is it not 3T*3T, or 3T^2? Is it some specific behavior of T that determines this?
T(n)=3∗3T(n−4) leading to the general form: T(n)=3kT(n−2k)
2) where does the above k variable come from, exactly? I understand that you'd combine the 3s to have 3^2, but how do you replace 3^2 with 3^k?
Thanks in advance!