Prove that the sequence a0 = 2, 3, 6, 14, 40, 152, 784, ... with general term an = (n+4) an-1 - 4n an-2 + (4n-8) an-3 is the sum of two well-known sequences.
Answer: n! + 2n.
This is not a nice problem. We know the answer is easy (because A1 is almost always easy), so we are looking for something simple. Just try subtracting off various simple series until you recognize the result. I was lucky: 152, 784 vaguely reminded me of 120, 720.
51st Putnam 1990
© John Scholes
3 Nov 1999