We need to give a recurrence relation for if is the number of different ways a path of length n is covered in a game which is played by moving a marker ahead either 2 or 3 steps on a linear path.
For we get
since marker is move ahead either 2 or 3 steps.
Since market is moved ahead 2 or 3 steps, the number of ways to move 2 steps is one.
Therefore, we get
Similarly, we get