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EXAMPLE
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For n = 3, the a(3) = 8 equilateral triangles are
(0,0,0), (1,1,0), and (1,0,1);
(0,0,0), (1,1,0), and (0,1,1);
(0,0,0), (1,0,1), and (0,1,1);
(1,0,0), (0,1,0), and (0,0,1);
(1,0,0), (0,1,0), and (1,1,1);
(1,0,0), (0,0,1), and (1,1,1);
(0,1,0), (0,0,1), and (1,1,1); and
(1,1,0), (1,0,1), and (0,1,1).
For n = 6, the a(6) = 2240 equilateral triangles are
(0,0,0,0,0,0),(0,0,0,0,1,1),(0,0,0,1,0,1); and
(0,0,0,0,0,0),(0,0,1,1,1,1),(1,1,0,0,1,1); and all of the equilateral triangles that can be generated by mapping these under the 2^6*6! symmetries of the 6-cube.
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