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A130748
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Place n points on each of the three sides of a triangle, 3n points in all; a(n) = number of triangles (nondegenerate) that can be constructed using these points (plus the 3 original vertices) as vertices.
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0
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17, 72, 190, 395, 711, 1162, 1772, 2565, 3565, 4796, 6282, 8047, 10115, 12510, 15256, 18377, 21897, 25840, 30230, 35091, 40447, 46322, 52740, 59725, 67301, 75492, 84322, 93815, 103995, 114886
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Binomial[3(n+1), 3] - 3*binomial[n+2, 3] where n>0
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EXAMPLE
| 5 points are put on each side of a triangle (n = 5); we then have 18 vertices to construct with: 5 * 3 + 3 originals. The number of total arrangements = combi(18,3) : combi[3(n+1),3]. But these include degenerates along the 3 sides: 7 points on each side, so combi(7,3) on each side : 3 * combi[n+2, 3] combi[18,3] - 3 * combi[7,3] = 816 - 105 = 711
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CROSSREFS
| Sequence in context: A050524 A087514 A119625 * A131692 A157864 A059704
Adjacent sequences: A130745 A130746 A130747 * A130749 A130750 A130751
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KEYWORD
| nonn
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AUTHOR
| Denis Borris (daborris(AT)rogers.com), Jul 12 2007
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