A166367 - OEIS

%I #19 Jun 08 2026 10:20:43

%S 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,

%T 9663676380,77309410752,618475283748,4947802251840,39582417869568,

%U 316659341795328,2533274725072896,20266197726265344,162129581215580160

%N Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%C The initial terms coincide with those of A003951, 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="/A166367/b166367.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 (7,7,7,7,7,7,7,7,7,7,-28).

%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)/(28*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).

%p seq(coeff(series((1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 13 2020

%t CoefficientList[Series[(1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12), {t,0,30}], t] (* _G. C. Greubel_, May 10 2016 *)

%t coxG[{11,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 07 2019 *)

%o (SageMath)

%o def A166367_list(prec):

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

%o     return P( (1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12) ).list()

%o A166367_list(30) # _G. C. Greubel_, Mar 13 2020

%o (PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)*(1+x)/(1-7*x-7*x^2-7*x^3-7*x^4-7*x^5-7*x^6-7*x^7-7*x^8-7*x^9-7*x^10+28*x^11)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 08 2026

%Y Cf. A003951, A154638.

%K nonn,easy,changed

%O 0,2

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