A166366 - OEIS

%I #14 Dec 03 2025 17:11:31

%S 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828856,

%T 2259801964,15818613552,110730293520,775112045232,5425784250768,

%U 37980489294384,265863421833744,1861043930247600,13027307353612944

%N Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%C The initial terms coincide with those of A003950, 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="/A166366/b166366.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 (6,6,6,6,6,6,6,6,6,6,-21).

%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)/(21*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

%p seq(coeff(series((1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 13 2020

%t CoefficientList[Series[(1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12), {t,0,30}], t] (* _G. C. Greubel_, May 10 2016 *)

%t coxG[{11, 21, -6}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 13 2020 *)

%o (SageMath)

%o def A166366_list(prec):

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

%o     return P( (1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12) ).list()

%o A166366_list(30) # _G. C. Greubel_, Mar 13 2020

%K nonn

%O 0,2

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