cp's OEIS Frontend

A168993 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%I A168993 #11 Nov 25 2016 10:26:43
%S A168993 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A168993 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A168993 4202649788315975388,113471544284531335476,3063731695682346057852
%N A168993 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
%C A168993 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A168993 First disagreement at index 23: a(23) = 865288322713713146133777970498434, A170747(23) = 865288322713713146133777970498812. - Klaus Brockhaus, Apr 19 2011
%C A168993 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168993 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A168993 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)/(351*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%t A168993 With[{num=Total[2t^Range[22]]+t^23+1,den=Total[-26 t^Range[22]]+ 351t^23+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 01 2012 *)
%Y A168993 Cf. A170747 (G.f.: (1+x)/(1-27*x)).
%K A168993 nonn
%O A168993 0,2
%A A168993 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009