cp's OEIS Frontend

A169143 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%I A169143 #10 Nov 25 2016 12:21:54
%S A169143 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A169143 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A169143 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A169143 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
%C A169143 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A169143 First disagreement at index 26: a(26) = 3121241797049096063956366389647016446001, A170753(26) = 3121241797049096063956366389647016446562. - Klaus Brockhaus, Apr 30 2011
%C A169143 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169143 <a href="/index/Rec#order_26">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, -528).
%F A169143 G.f.: (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^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 A169143 With[{num=Total[2t^Range[25]]+t^26+1,den=Total[-32 t^Range[25]]+528t^26+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Aug 21 2013 *)
%Y A169143 Cf. A170753 (G.f.: (1+x)/(1-33*x)).
%K A169143 nonn
%O A169143 0,2
%A A169143 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009