cp's OEIS Frontend

A275787 Number of cells in the two-sided Coxeter complex of type B_n.

%I A275787 #29 Mar 12 2024 15:33:23
%S A275787 1,5,41,509,8469,176217,4400325,128203049,4268957449,159922273421,
%T A275787 6656731517249,304797275277365,15224868078068845,823874409422614577,
%U A275787 48012621942105876301,2997884066292303095889,199666128081901473290833,14129411123649333432720277,1058688691179737704258634521,83732563305101190468369022317,6971039973751002759723517967941
%N A275787 Number of cells in the two-sided Coxeter complex of type B_n.
%C A275787 a(n) is the number of nonnegative integer matrices with sum of entries equal to 2*n-2 (or 2*n-1), no zero rows or columns, which are centrally symmetric. - _Ludovic Schwob_, Feb 17 2024
%H A275787 Evgeniy Krasko, <a href="https://arxiv.org/abs/1709.00796">Counting Unlabelled Chord Diagrams of Maximal Genus</a>, arXiv:1709.00796 [math.CO], 2017.
%H A275787 T. K. Petersen, <a href="http://arxiv.org/abs/1607.00086">A two-sided analogue of the Coxeter complex</a>, arXiv:1607.00086 [math.CO], 2016.
%e A275787 The a(2) = 5 matrices whose sum of entries is equal to 2:
%e A275787   [2] [1 1]
%e A275787 .
%e A275787   [1] [1 0] [0 1]
%e A275787   [1] [0 1] [1 0]
%p A275787 B:=proc(n) local f;
%p A275787 option remember;
%p A275787 if n=1 then 1+s*t;
%p A275787 elif n>1 then
%p A275787 f:=B(n-1);
%p A275787 RETURN(simplify( (2*n*s*t-s*t+1)*f+(2*s*t*(1-s)+s/n*(1-s)*(1-t))*diff(f,s) + (2*s*t*(1-t)+t/n*(1-s)*(1-t))*diff(f,t) + 2/n*s*t*(1-s)*(1-t)*diff( diff(f,s),t) ));
%p A275787 fi;
%p A275787 end:
%p A275787 seq(eval(eval(subs(s=x/(1+x),t=y/(1+y), B(n))*(1+x)^n*(1+y)^n,y=1),x=1), n=1..30);
%t A275787 B[n_] := B[n] = Which[n == 1, 1 + s*t, n > 1, f = B[n - 1]; Return[ Simplify[ (2*n*s*t - s*t + 1)*f + (2*s*t*(1 - s) + s/n*(1 - s)*(1 - t))*D[f, s] + (2*s*t*(1 - t) + t/n*(1 - s)*(1 - t))*D[f, t] + 2/n*s*t*(1 - s)*(1 - t)*D[ D[f, s], t]]]];
%t A275787 Join[{1}, Table[bn = ((B[n] /. {s -> x/(1 + x), t -> y/(1 + y)})*(1 + x)^n*(1 + y)^n /. {y -> 1, x -> 1}); Print[bn]; bn, {n, 1, 20}]] (* _Jean-François Alcover_, Nov 27 2017, from Maple *)
%Y A275787 Cf. A120733 gives the number of cells for type A_n.
%K A275787 nonn
%O A275787 1,2
%A A275787 _Kyle Petersen_, Aug 09 2016