A frog is placed at the origin on the number line, and moves according to the following rule: in a given move, the frog advances to either the closest point with a greater integer coordinate that is a multiple of $$3$$, or to the closest point with a greater integer coordinate that is a multiple of $$13$$. A move sequence is a sequence of coordinates which correspond to valid moves, beginning with $$0$$, and ending with $$39$$. For example, $$0,\ 3,\ 6,\ 13,\ 15,\ 26,\ 39$$ is a move sequence. How many move sequences are possible for the frog?

(第二十五届AIME1 2007 第6题)