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%I #19 Jun 13 2015 00:50:26
%S 0,0,0,1,0,5,2,14,8,30,20,55,40,91,70,140,112,204,168,285,240,385,330,
%T 506,440,650,572,819,728,1015,910,1240,1120,1496,1360,1785,1632,2109,
%U 1938,2470,2280
%N Number of acute triangles made from vertices of a regular n-gon.
%H Vincenzo Librandi, <a href="/A060422/b060422.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F a(n) = n*(n+1)*(n-1)/24 when n is odd, otherwise n*(n-2)*(n-4)/24.
%F G.f.: x^3*(2*x^2-x+1) / ((x-1)^4*(x+1)^3). - _Colin Barker_, Dec 24 2012
%F a(n) = n*(2*n^2-6*n+7-3*(2*n-3)*(-1)^n)/48. - _Luce ETIENNE_, Mar 19 2015
%t LinearRecurrence[{1, 3, -3, -3, 3, 1, -1},{0, 0, 0, 1, 0, 5, 2}, 50] (* _Vincenzo Librandi_, Dec 25 2012 *)
%Y Union of A000330, A007290.
%K easy,nonn
%O 0,6
%A _Sen-Peng Eu_, Apr 05 2001
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