Question: A-3-2. (10 marks} For both (a) and (b): write S in set notation; determine the generating series os(x) (simplify your expression); and determine the recurrence

A-3-2. (10 marks} For both (a) and (b): write S in

A-3-2. (10 marks} For both (a) and (b): write S in set notation; determine the generating series os(x) (simplify your expression); and determine the recurrence relation and initial conditions for the coefficients an of Os(2). Clearly state all uses of the sum/product/string lemmas and which one you are using. The weight function in each is the standard one: the sum of the parts. (a) S is the set of compositions with any number of parts where each part is in {1,3}. (b) S is the set of compositions with any number of parts where each part is at least 7. A-3-2. (10 marks} For both (a) and (b): write S in set notation; determine the generating series os(x) (simplify your expression); and determine the recurrence relation and initial conditions for the coefficients an of Os(2). Clearly state all uses of the sum/product/string lemmas and which one you are using. The weight function in each is the standard one: the sum of the parts. (a) S is the set of compositions with any number of parts where each part is in {1,3}. (b) S is the set of compositions with any number of parts where each part is at least 7

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