A060422 Number of acute triangles made from vertices of a regular n-gon.

0, 0, 0, 1, 0, 5, 2, 14, 8, 30, 20, 55, 40, 91, 70, 140, 112, 204, 168, 285, 240, 385, 330, 506, 440, 650, 572, 819, 728, 1015, 910, 1240, 1120, 1496, 1360, 1785, 1632, 2109, 1938, 2470, 2280

Offset: 0

Author

Sen-Peng Eu, Apr 05 2001

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Crossrefs

Union of A000330, A007290.

Programs

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1},{0, 0, 0, 1, 0, 5, 2}, 50] (* Vincenzo Librandi, Dec 25 2012 *)

Formula

a(n) = n*(n+1)*(n-1)/24 when n is odd, otherwise n*(n-2)*(n-4)/24.

G.f.: x^3*(2*x^2-x+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Dec 24 2012

a(n) = n*(2*n^2-6*n+7-3*(2*n-3)*(-1)^n)/48. - Luce ETIENNE, Mar 19 2015