Question: Finding the number of possible melodies.

In Denys Parsons’ Directory of Tunes and Musical Themes, melodies fro more than 14,000 songs are listed according to the following scheme: the first note of every song is represented by an asterisk *, and successive notes are represented by R (for repeat the previous note), U (for a note that goes up), or D (for a note that goes down). Beethoven’s Fifth Symphony begins as *RDD. Classical melodies are represented through the first 16 notes. With this scheme, how many different classical melodies are possible?