Consider the following recurrence relation: T (1) = 6, and for n > 1, T (n) = 1 + 2T ([n/2]) Note. [x] is the the floor function. It rounds x down to the nearest integer. (a) Determine the value for T (n) for integers n from 1 to 8. (b) Expand the recurrence relation to get the closed form. Show your work; do not just show the final equation. For arithmetic simplicity, you may assume n is a sufficiently large power of 2 such that the floor function does not lead to rounding issues.