# Sequences

Number Theory Level pending

Let $$S$$ be the set of all ordered triplets 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 $${ a }_{ n }={ a }_{ n-1 }\cdot \left| { a }_{ n-2 }-{ a }_{ n-3 } \right|$$ for all $$n\ge 4$$. Find the number of such sequences for which $$a_n=0$$ for some value of $$n$$.

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