2015 AIME I Problem 9

Let S be the set of all ordered triple of integers (a_1,a_2,a_3) with 1 \le a_1,a_2,a_3 \le 10. Each ordered triple in S generates a sequence according to the rule a_n=a_{n-1}\cdot | a_{n-2}-a_{n-3} | for all n\ge 4. Find the number of such sequences for which a_n=0 for some n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.