This problem is about finite sequences where all the terms are positive integers.

One such sequence is 3, 1, 1, 2. The sequence sum for this series is 7, because

                                                 3 + 1 + 1 + 2 = 7.

How many of this kind of sequence have sequence sum 3? Or of 4? Or 5? Or 6?

Can you generalise to say how many of this kind of sequence have sequence sum n, if n is a positive integer? Explain your reasoning carefully.