In Denys Parsons' Directory of Tunes and Musical Themes, melodies for 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), 17 (for a note that goes up), or D (for a note that goes down). Beethoven's Fifth Symphony begins as *RRD. Classical melodies are represented through the first 16 notes. With this scheme, how many different classical melodies are possible?