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A211380
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Number of pairs of intersecting diagonals in the interior and exterior of a regular n-gon.
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2
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0, 1, 5, 15, 42, 94, 189, 340, 572, 903, 1365, 1981, 2790, 3820, 5117, 6714, 8664, 11005, 13797, 17083, 20930, 25386, 30525, 36400, 43092, 50659, 59189, 68745, 79422, 91288, 104445, 118966, 134960, 152505, 171717, 192679, 215514, 240310, 267197, 296268, 327660
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OFFSET
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3,3
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LINKS
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FORMULA
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a(n) = 1/8*n*(n^3-11*n^2+43*n-58) for n even;
a(n) = 1/8*n*(n-3)*(n^2-8*n+19) for n odd.
G.f.: x^4*(2*x^5-3*x^4-7*x^3-x^2-2*x-1) / ((x-1)^5*(x+1)^2). [Colin Barker, Feb 14 2013]
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MAPLE
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a:=n->piecewise(n mod 2 = 0, 1/8*n*(n^3-11*n^2+43*n-58), n mod 2 = 1, 1/8*n*(n-3)*(n^2-8*n+19), 0);
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MATHEMATICA
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Drop[CoefficientList[Series[x^4(2x^5-3x^4-7x^3-x^2-2x-1)/((x-1)^5(x+1)^2), {x, 0, 50}], x], 3] (* or *) LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 5, 15, 42, 94, 189}, 50] (* Harvey P. Dale, Dec 03 2022 *)
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PROG
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(Python)
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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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