An equilateral triangle lies in the plane with two of its vertices at the points

*(0, 0)*and*(n, 0)*, where*n*is an integer. Determine the number of points*(x, y)*with integer coordinates that lie in the interior of the triangle.Your final answer should be a formula that relates the total number of lattice points

*(x, y)*, call it*N*, to the x-coordinate,*n*. Note also that the lattice points must lie*within*the triangle and not along its perimeter.Have fun!

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