Find a recursion relation

Question

Given an unlimited supply of M & M's and of bugglegum, which cost one cent each, and of sourballs, peppermints, and gumdrops, which cost two cents each. You are going to buy n cents worth of candy, one piece at atime. Leta_{n be the number of selection sequences that end up costing n cents.So}a_{2 = 7 ( mm,mb, bb, bm, s, p, g). Order matters.}

_{Find a recursion relationfor} a_{n. Solve the recursion. Find a formula for} a_n.