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A166258 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166258 #14 Mar 11 2020 19:06:20
%S A166258 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A166258 14367501434880,632170063134720,27815482777926690,1223881242228730800,
%U A166258 53850774658062239550,2369434084954654251600,104255099738001078372000
%N A166258 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166258 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A166258 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166258 G. C. Greubel, <a href="/A166258/b166258.txt">Table of n, a(n) for n = 0..500</a>
%H A166258 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A166258 G.f.: (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)/(946*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%p A166258 seq(coeff(series((1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166258 CoefficientList[Series[(1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 08 2016 *)
%t A166258 coxG[{10, 946, -43}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166258 (Sage)
%o A166258 def A166258_list(prec):
%o A166258     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166258     return P( (1+t)*(1-t^10)/(1-44*t+989*t^10-946*t^11) ).list()
%o A166258 A166258_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166258 nonn
%O A166258 0,2
%A A166258 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009