%I A156231
%S A156231 1,0,6,8,24,48,106,192,369,624,1080,1728,2787,4248,6498,9528,13962,
%T A156231 19824,28066,38760,53334,71936,96618,127680,167983,218040,281784,360024,
%U A156231 458037,577080,724098,900936,1116636,1373808,1684038
%N A156231 Sequence gives the Poincare series of an ordinal Hodge algebra, or algebra 
               with straightening law, for a ring that the braid group on four strands 
               acts on. It is Cohen-Macaulay
%D A156231 Stephen P. Humphries, Action of some braid groups on Hodge algebras. 
               Comm. Algebra 26 (1998), no. 4, pages 1233-1242. See Proposition 
               3.4
%F A156231 G.f. 1-(-4*x^20+8*x^19+6*x^18-12*x^17-11*x^16-2*x^15+25*x^14+10*x^13-12*x^12)/
               ((1+x+x^2)^2*(1+x)^5*(1+x^2)*(1-x)^9)-(-14*x^11-15*x^10+14*x^9+17*x^8+4*x^7-16*x^6-12*x^5+10*x^4+4*x^3-6*\
               x^2)/((1+x+x^2)^2*(1+x)^5*(1+x^2)*(1-x)^9)
%e A156231 For n=2 the dimension of the degree two part is 6.
%Y A156231 A053090 is a similar Poincare series for a ring on which the three strand 
               braid groups acts.
%Y A156231 Sequence in context: A005887 A119875 A053189 this_sequence A024860 A025100 
               A155478
%Y A156231 Adjacent sequences: A156228 A156229 A156230 this_sequence A156232 A156233 
               A156234
%K A156231 nonn
%O A156231 0,3
%A A156231 Stephen Humphries (steve(AT)math.byu.edu), Feb 06 2009