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 A211380 Number of pairs of intersecting diagonals in the interior and exterior of a regular n-gon. 1

%I

%S 0,1,5,15,42,94,189,340,572,903,1365,1981,2790,3820,5117,6714,8664,

%T 11005,13797,17083,20930,25386,30525,36400,43092,50659,59189,68745,

%U 79422,91288,104445,118966,134960,152505,171717,192679,215514,240310,267197,296268,327660

%N Number of pairs of intersecting diagonals in the interior and exterior of a regular n-gon.

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/RegularPolygonDivisionbyDiagonals.html">Regular Polygon Division by Diagonals</a> (MathWorld).

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).

%F a(n) = 1/8*n*(n^3-11*n^2+43*n-58) for n even;

%F a(n) = 1/8*n*(n-3)*(n^2-8*n+19) for n odd.

%F a(n) = A176145(n) - A211379(n).

%F 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]

%p 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);

%Y Cf. A176145, A211379.

%K nonn,easy

%O 3,3

%A _Martin Renner_, Feb 07 2013

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Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)