1. Start conjecturing about yams if you haven't already. Do you see a possible recurrence relation? How about a closed-form formula? Try to prove any yammy conjectures you have. Again, because you only began with a yam and a laser cutter, this information must be used in your proofs.
2. Combine all the information you have into one table:
Does viewing this information together cause any new patterns to appear? What might go in that bottom row of the table? Have you any new conjectures? Do you see any connection to binomial coefficients?