Question 6
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?