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A166364 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166364 #15 Mar 13 2020 08:38:26
%S A166364 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593735,
%T A166364 292968600,1464842640,7324211400,36621048000,183105195000,
%U A166364 915525750000,4577627625000,22888132500000,114440634375000,572203031250000
%N A166364 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166364 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A166364 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166364 G. C. Greubel, <a href="/A166364/b166364.txt">Table of n, a(n) for n = 0..500</a>
%H A166364 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,4,4,4,4,4,4,4,4,-10).
%F A166364 G.f.: (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)/(10*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
%p A166364 seq(coeff(series((1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 13 2020
%t A166364 CoefficientList[Series[(1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), {t,0,30}], t] (* _G. C. Greubel_, May 10 2016 *)
%t A166364 coxG[{11,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 13 2016 *)
%o A166364 (Sage)
%o A166364 def A166364_list(prec):
%o A166364     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166364     return P( (1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12) ).list()
%o A166364 A166364_list(30) # _G. C. Greubel_, Mar 13 2020
%K A166364 nonn
%O A166364 0,2
%A A166364 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009