Sequences

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 $n$ .