Integer Partitions

Imagine that you're working at a large chain bookstore, and you've just gotten a hundred copies of the latest bestseller. You are assigned to shelve them. No problem, except that each shelf only holds at most thirty books. Again, no problem: you can put 30 each on three shelves, and 10 on a fourth shelf. Or you could put 25 each on four shelves... or maybe 20 each on five shelves... or if you were feeling really disgruntled, you could put one copy on each of a hundred different shelves, scattered around the store.

Now, in case you weren't already disgruntled, the manager tells you that if none of the books sell on a given day, you are to reshelve them differently the next day, and again the next day, until they start selling. How many ways are there to arrange these things? (Hint: try small numbers first!)