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A166230 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166230 #14 Mar 11 2020 21:26:30
%S A166230 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A166230 8179679503002,335366859623082,13750041244545501,563751691026330240,
%U A166230 23113819332078093360,947666592615142522080,38854330297218411872400
%N A166230 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166230 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A166230 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166230 G. C. Greubel, <a href="/A166230/b166230.txt">Table of n, a(n) for n = 0..500</a>
%H A166230 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A166230 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)/(820*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).
%p A166230 seq(coeff(series((1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166230 CoefficientList[Series[(1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 07 2016 *)
%t A166230 coxG[{10, 820, -40}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166230 (Sage)
%o A166230 def A166230_list(prec):
%o A166230     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166230     return P( (1+t)*(1-t^10)/(1-41*t+860*t^10-820*t^11) ).list()
%o A166230 A166230_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166230 nonn
%O A166230 0,2
%A A166230 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009