%I #26 May 28 2022 04:02:00

%S 0,0,0,0,0,5,6,21,24,54,60,110,120,195,210,315,336,476,504,684,720,

%T 945,990,1265,1320,1650,1716,2106,2184,2639,2730,3255,3360,3960,4080,

%U 4760,4896,5661,5814,6669,6840,7790,7980,9030,9240,10395,10626

%N Number of obtuse triangles made from vertices of a regular n-gon.

%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-3)/8 when n odd; n*(n-2)*(n-4)/8 when n even.

%F G.f.: x^5*(x+5)/((1-x)(1-x^2)^3). - _Michael Somos_, Jan 30 2004

%F For n odd, a(n) = A080838(n). - _Gerald McGarvey_, Sep 14 2008

%F a(n) = n*(2*n-3-(-1)^n)*(2*n-7-(-1)^n)/32. - _Wesley Ivan Hurt_, Dec 31 2013

%F E.g.f.: x*((x - 3)*x*cosh(x) + (x^2 - x + 3)*sinh(x))/8. - _Stefano Spezia_, May 28 2022

%p A060423:=n->n*(2*n-3-(-1)^n)*(2*n-7-(-1)^n)/32; seq(A060423(n), n=0..100); # _Wesley Ivan Hurt_, Dec 31 2013

%t Table[n(2n-3-(-1)^n)(2n-7-(-1)^n)/32, {n, 0, 100}] (* _Wesley Ivan Hurt_, Dec 31 2013 *)

%t Table[If[EvenQ[n],(n(n-2)(n-4))/8,(n(n-1)(n-3))/8],{n,0,50}] (* _Harvey P. Dale_, Sep 18 2018 *)

%o (PARI) a(n)=polcoeff(x^5*(5+x)/(1-x)/(1-x^2)^3+x*O(x^n),n)

%o (Magma) [n*(2*n-3-(-1)^n)*(2*n-7-(-1)^n)/32 : n in [0..60]]; // _Wesley Ivan Hurt_, Apr 14 2017

%Y Cf. A000330, A007290, A046092, A080838.

%K easy,nice,nonn

%O 0,6

%A _Sen-Peng Eu_, Apr 05 2001