cp's OEIS Frontend

A169121 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%I A169121 #11 Nov 25 2016 12:15:50
%S A169121 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A169121 28295372292,311249095212,3423740047332,37661140520652,
%U A169121 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A169121 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
%C A169121 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A169121 First disagreement at index 26: a(26) = 1300164713206604664501962946, A003954(26) = 1300164713206604664501963012. - Klaus Brockhaus, Apr 30 2011
%C A169121 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169121 <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).
%F A169121 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)/(55*t^26 - 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 - 10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
%t A169121 With[{num=Total[2t^Range[25]]+t^26+1,den=Total[-10 t^Range[25]]+55t^26+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 10 2012 *)
%Y A169121 Cf. A003954 (G.f.: (1+x)/(1-11*x)).
%K A169121 nonn
%O A169121 0,2
%A A169121 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009