1. Let i, j, k, n be positive integers. Suppose that a total of i+2j + 2k people need to pay a bill for n dollars. Of these people: i are willing to pay any positive integer amount of dollars, j are only willing to pay 1 or 2 dollars, another j are willing to pay any positive odd integer amount of dollars, k are willing to pay 2 or 3 dollars, and another k are willing to pay any positive even integer amount of dollars. Find with induction proof the number of ways to split the bill as a function of i, j, k, and n.