2007 AIME II Problem 6

An integer is called *parity-monotonic* if its decimal representation a_{1}a_{2}a_{3}\cdots a_{k} satisfies a_{i}<a_{i+1} if a_{i} is odd, and a_{i}>a_{i+1} if a_{i} is even. How many four-digit parity-monotonic integers are there?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.