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%I #20 Mar 12 2020 08:43:34
%S 1,3,6,12,24,48,96,192,384,768,1536,3069,6132,12255,24492,48948,97824,
%T 195504,390720,780864,1560576,3118848,6233094,12456993,24895608,
%U 49754487,99435570,198724440,397155696,793725456,1586279904,3170219520
%N Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C The initial terms coincide with those of A003945, 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="/A166327/b166327.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-1,2,-1,2,-1,2,-1).
%F G.f.: (t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1) / (t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1).
%p seq(coeff(series((1+t)*(1-t^11)/(1-2*t+2*t^11-t^12), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Mar 12 2020
%t CoefficientList[Series[(1+t)*(1-t^11)/(1-2*t+2*t^11-t^12), {t,0,30}], t] (* _G. C. Greubel_, May 09 2016 *)
%o (Sage)
%o def A166327_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P( (1+t)*(1-t^11)/(1-2*t+2*t^11-t^12) ).list()
%o A166327_list(30) # _G. C. Greubel_, Aug 10 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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