Puzzle #164: Entertaining the Cat

Your cat, Empress, can be kept entertained by a mouse for 15 minutes, by catnip for 30 minutes, and by a guinea pig for 1 1/2 hours. Humans are just so boring, and besides, one requires staff. Empress has a grueling daily schedule of 18 hours sleep, 3 hours grooming, and 1/2 hour eating. The remainder of the day is for entertainment. A mouse costs $1, a dose of catnip costs $3, and a guinea pig costs $15; these rates are per use. The animals are stuffed toys, but Empress is rather hard on her toys.

In a given day, you can not have the same entertainment twice in a row or more than twice, and you must spend over $20 (unless you really did not like those curtains). Leftover entertainment time is not allowed.

How many possible entertainment programs are there for Empress if you want to keep your curtains?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, July 27, 2016 at noon Pacific Time. I will post the answer shortly after.