cp's OEIS Frontend

A168996 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%I A168996 #10 Nov 25 2016 10:27:37
%S A168996 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A168996 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A168996 16474671000000000000,494240130000000000000,14827203900000000000000
%N A168996 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
%C A168996 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A168996 First disagreement at index 23: a(23) = 9728128478789999999999999999999535, A170750(23) = 4465573156292499073180156937317230. - Klaus Brockhaus, Apr 19 2011
%C A168996 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168996 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A168996 G.f.: (t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
%t A168996 With[{num=Total[2t^Range[22]]+t^23+1,den=Total[-29 t^Range[22]]+ 435t^23+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 04 2013 *)
%Y A168996 Cf. A170750 (G.f.: (1+x)/(1-30*x)).
%K A168996 nonn
%O A168996 0,2
%A A168996 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009