1994 AIME Problem 6

The graphs of the equations

y=k, \qquad y=\sqrt{3}x+2k, \qquad y=-\sqrt{3}x+2k,

are drawn in the coordinate plane for k=-10,-9,-8,\ldots,9,10.\, These 63 lines cut part of the plane into equilateral triangles of side 2/\sqrt{3}. How many such triangles are formed?

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.