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A234250
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Number of ways to choose 3 points in an n X n X n triangular grid so that they do not form a 2 X 2 X 2 triangle.
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4
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0, 16, 111, 439, 1305, 3240, 7091, 14126, 26154, 45660, 75955, 121341, 187291, 280644, 409815, 585020, 818516, 1124856, 1521159, 2027395, 2666685, 3465616, 4454571, 5668074, 7145150, 8929700, 11070891, 13623561, 16648639, 20213580, 24392815, 29268216, 34929576
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OFFSET
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2,2
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LINKS
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FORMULA
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a(n) = (n - 1)*(n - 2)*(n^4 + 6*n^3 + 13*n^2 + 16*n - 24)/48.
G.f.: x^3*(x^4-3*x^3+2*x^2+x-16) / (x-1)^7. - Colin Barker, Feb 05 2014
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MATHEMATICA
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LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 16, 111, 439, 1305, 3240, 7091}, 40] (* Harvey P. Dale, Mar 09 2019 *)
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PROG
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(PARI) Vec(x^3*(x^4-3*x^3+2*x^2+x-16)/(x-1)^7 + O(x^100)) \\ Colin Barker, Feb 05 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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