A166364 - OEIS

%I #15 Mar 13 2020 08:38:26

%S 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593735,

%T 292968600,1464842640,7324211400,36621048000,183105195000,

%U 915525750000,4577627625000,22888132500000,114440634375000,572203031250000

%N 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 The initial terms coincide with those of A003948, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A166364/b166364.txt">Table of n, a(n) for n = 0..500</a>

%H <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 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 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 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 coxG[{11,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 13 2016 *)

%o (Sage)

%o def A166364_list(prec):

%o     P.<t> = PowerSeriesRing(ZZ, prec)

%o     return P( (1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12) ).list()

%o A166364_list(30) # _G. C. Greubel_, Mar 13 2020

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009