# Triangulating A Triangle Of Coins!

A triangles has a non-negative integer $$n$$ coins on all its sides as demonstrated above for $$n=9$$. For how many values of $$n<1000$$ can we build such a triangle with side-length $$n$$ using only the below coin triangles?

Determine the rule for $$n$$ for which it is possible to tile the triangle.

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