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%I A166365 #12 Mar 13 2020 07:12:02
%S A166365 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A166365 423263211,2539579140,15237474105,91424840220,548549014860,
%U A166365 3291293930400,19747762629840,118486570063680,710919386089920,4265516110786560
%N A166365 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166365 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A166365 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166365 G. C. Greubel, <a href="/A166365/b166365.txt">Table of n, a(n) for n = 0..500</a>
%H A166365 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (5,5,5,5,5,5,5,5,5,5,-15).
%F A166365 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)/(15*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%p A166365 seq(coeff(series((1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 13 2020
%t A166365 CoefficientList[Series[(1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12), {t,0,30}], t] (* _G. C. Greubel_, May 10 2016 *)
%t A166365 coxG[{11, 15, -5}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 13 2020 *)
%o A166365 (Sage)
%o A166365 def A166365_list(prec):
%o A166365     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166365     return P( (1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12) ).list()
%o A166365 A166365_list(30) # _G. C. Greubel_, Aug 10 2019
%K A166365 nonn
%O A166365 0,2
%A A166365 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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