A220882 - OEIS

%I #14 Dec 02 2017 10:07:49

%S 1,2,16,93,505,2548,12400,58140,266550,1198564,5312032,23263695,

%T 100910001,434217000,1855972096,7887862224,33359979546,140492933100,

%U 589495272736,2465455090098,10281760786682,42768958597992,177499631598976,735146520745000,3039095720959424,12542491305496152

%N Number of (n - 6)-dissections of an n-gon (equivalently, the number of three-dimensional faces of the (n-3)-dimensional associahedron) modulo the cyclic action.

%H Douglas Bowman and Alon Regev, <a href="http://arxiv.org/abs/1209.6270">Counting symmetry classes of dissections of a convex regular polygon</a>, arXiv preprint arXiv:1209.6270 [math.CO], 2012.

%F See Maple code.

%p C:=n->binomial(2*n,n)/(n+1);

%p T4:=proc(n) local t1; global C;

%p t1 :=  (((n-3)*(n-4)^2*(n-5))/(24*n*(2*n-5)))*C(n-2);

%p if n mod 2 = 0 then t1:=t1+((n-4)^2/(4*n))*C(n/2-2) fi;

%p if n mod 3 = 0 then t1:=t1+((n-3)/9)*C(n/3-1) fi;

%p if n mod 6 = 0 then t1:=t1+C(n/6-1)/3 fi;

%p t1; end;

%p [seq(T4(n),n=6..40)];

%t c = CatalanNumber;

%t T4[n_] := Module[{t1},

%t t1 = (((n - 3)*(n - 4)^2*(n - 5))/(24*n*(2*n - 5)))*c[n - 2];

%t If[Mod[n, 2] == 0, t1 = t1 + ((n - 4)^2/(4*n))*c[n/2 - 2]];

%t If[Mod[n, 3] == 0, t1 = t1 + ((n - 3)/9)*c[n/3 - 1]];

%t If[Mod[n, 6] == 0, t1 = t1 + c[n/6 - 1]/3]; t1];

%t Table[T4[n], {n, 6, 40}] (* _Jean-François Alcover_, Dec 02 2017, from Maple *)

%Y Cf. A003444, A003445, A003450, A220881.

%K nonn

%O 6,2

%A _N. J. A. Sloane_, Dec 28 2012