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A244501
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Number of ways to place 3 points on an n X n X n triangular grid so that no pair of them has distance sqrt(3).
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4
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1, 8, 55, 248, 820, 2212, 5163, 10815, 20833, 37540, 64067, 104518, 164150, 249568, 368935, 532197, 751323, 1040560, 1416703, 1899380, 2511352, 3278828, 4231795, 5404363, 6835125, 8567532, 10650283, 13137730, 16090298, 19574920, 23665487, 28443313, 33997615
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OFFSET
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2,2
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COMMENTS
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sqrt(3) is the second closest (Euclidean) distance for a pair of points in a triangular grid. For illustration see A244500.
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LINKS
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FORMULA
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a(n) = 1/48*n^6 + 1/16*n^5 - 13/16*n^4 + 61/48*n^3 + 247/24*n^2 - 293/6*n + 6 for n >= 3.
G.f.: -x^2*(6*x^7 - 17*x^6 + 14*x^5 - 6*x^4 - 4*x^3 + 20*x^2 + x + 1) / (x-1)^7. - Colin Barker, Jun 29 2014
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MATHEMATICA
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CoefficientList[Series[-(6*x^7-17*x^6+14*x^5-6*x^4-4*x^3+20*x^2+x+1) / (x-1)^7, {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 03 2014 after Colin Barker *)
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PROG
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(PARI) Vec(-x^2*(6*x^7-17*x^6+14*x^5-6*x^4-4*x^3+20*x^2+x+1)/(x-1)^7 + O(x^100)) \\ Colin Barker, Jun 29 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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