%I #16 Mar 11 2020 21:26:41
%S 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T 11960018888708,514280812214444,22114074925220146,950905221784425600,
%U 40888924536728552592,1758223755079252588512,75603621468404628869424
%N Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A170763, 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="/A166254/b166254.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F 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)/(903*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-43*t+945*t^10-903*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-43*t+945*t^10-903*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 08 2016 *)
%t coxG[{10,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 18 2018 *)
%o (Sage)
%o def A166254_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P( (1+t)*(1-t^10)/(1-43*t+945*t^10-903*t^11) ).list()
%o A166254_list(30) # _G. C. Greubel_, Aug 10 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009