Let n 2 0. We want to answer this question: How many integer compositions of n have either 3 or 4 parts, where the first part is even, and the last part is at most 100? (3) Find an expression for a set C of all relevant integer compositions. (b) Write down an appropriate weight function to for C. c Determine the generating series of C with respect to to. Express your answer in the form @ where a: a: are P a 9' q(m) polynomials. Simplify as much as possible. Remember to justify every step. Note: You may use the following formula regarding formal power series without proof. For any I: 2 0, 1 _ $k+l 1+w+m2+---+a:'\"= 1:1': (d) Determine the answer to the original question in terms of your formula from part (c). (e) Derive an explicit formula to the original question for even values of n 2 104, and simplify as much as possible. The end result should be a polynomial in n of degree 2