Suppose that at the interstellar buffet you are allowed to make a plate with any amount of items, but there are some strict rules for how to make your plate. You can have any number of Alpops and Cushwools as you like. You must take an even number of Bleeblebloops. You can have up to 5 Duwops. The chef is insecure so you need to take at least one of their speciality dish, the Eatawobblipop. Whenever a Filliplywoo and a Goobalobidopilop are on the same plate there is a violent chemical reaction, so you can't take both items. Fillipywoos are very expensive so the buffet limits 3 per customer. You snuck your friend Jeffrey in your pocket (he is an anarchist and doesn't like to pay for buffets) and he'd like you to bring him a piece of Haddock. You don't like Haddock so you'll just bring one piece for him. Write a generating function whose coefficients of 2" give the number of possible plates you can make with n items. You need to describe how and why you are making this generating function, or you will not receive full marks