Supposedly simple statistics problem

[jazzmminister]

I am having trouble with what seems to be a simple combinations or permutations problem as follows: Melodies for more than 14,000 songs are listed according to the following scheme" The first note of every song is represented by anasterisk * and successive notes are represented by R (for repeat of previous note), U (for a note that goes up), or D (for a note that goes down).
Classical melodies are represented through the first 16 notes. With this scheme, how many classical melodies are possible?
Any help or hints on this will be appreciated.
Thanks,
jw

 

[mathman]

Your description sounds a bit odd, since note changes can take any number of steps. However your description seems to allow only 3 possibilities (R, U, D) at each stage. In that case there are 3¹⁵ possibilities after 15 changes.