I have a set of super poker cards, consisting of an infinite number of cards. For each positive integer p, there are exactly four cards whose value is p: Spade(S), Heart(H), Club(C) and Diamond(D). There are no cards of other values.
Given two positive integers n and k, how many ways can you pick up at most k cards whosevalues sum to n? For example, if n=15 and k=3, one way is 3H + 4S + 8H, shown below: 