cp's OEIS Frontend

A169191 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169191 #16 Nov 25 2016 14:02:06
%S A169191 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A169191 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A169191 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A169191 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169191 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A169191 First disagreement at index 27: a(27) = 103000979302620170110560090858351542735985, A170753(27) = 103000979302620170110560090858351542736546. - _Klaus Brockhaus_, May 07 2011
%C A169191 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169191 Vincenzo Librandi, <a href="/A169191/b169191.txt">Table of n, a(n) for n = 0..200</a>
%H A169191 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
%F A169191 G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*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)/(528*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 - 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%t A169191 With[{num=Total[2t^Range[26]]+t^27+1,den=Total[-32 t^Range[26]]+528t^27+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 22 2014 *)
%Y A169191 Cf. A170753 (G.f.: (1+x)/(1-33*x)).
%K A169191 nonn
%O A169191 0,2
%A A169191 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009