8. Fix an integer k _ 1. Consider the sequence {hn}no that satisfies the recurrence k 0 = (n 2 k), 1= 0 ho = h1 = . . . = hk-2 =0, hk-1 = 1. (i) (5 points) Solve the recurrence, to find hn in closed form in terms of n and k. (ii) (5 points) Prove that your answer to (i) is correct