For a positive integer n≥3 plot n equally spaced points around a circle. Label one of them A, and place a marker at A. One may move the marker forward in a clockwise direction to either the next point or the point after that. Hence there are a total of 2n distinct moves available; two from each point. Let an count the number of ways to advance around the circle exactly twice, beginning and ending at A, without repeating a move. Prove that an−1+an=2n for all n≥4. AMCUSA(J)MOUSAMOinduction