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)