For each n 2 0, dene an to be the number of integer compositions of n where every part is congruent to 1 modulo 3, and define 1),, to be the number of integer compositions of n where every part is at least 3. For parts (a) and (b) below, express your answer in the form [3"] % where 19(32), q(:1:) are polynomials. You need to dene a relevant set, a weight function, and then determine the generating series. Remember to justify every step. (a) Determine an. (b) Determine b\". (c) Use parts (a) and (b) to prove that for any n 2 1, an = \"+2. That is, the number of compositions of n where every part is congruent to 1 modulo 3 is the same as the number of compositions of n | 2 where every part is at least 3