Problem 4 Day Trader’s Decisions

A day trader wants to trade n · 100 shares of the stock AAPL in blocks of 100. Temporary market rules prevent her from short-selling; in other words, she must own a block of shares before selling them. To avoid price slippage from large orders, she can only buy or sell 100 shares, i.e., 1 block, at a time. At the end of the day, she wants to own zero shares of AAPL.

How many ways can she do her trading? For example, when n = 2, she can do "BUY, SELL, BUY, SELL" or "BUY, BUY, SELL, SELL" and so there are 2 ways. Present your answer as a recurrence and clearly explain why the recurrence captures this number.