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A166130 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166130 #23 Sep 28 2024 14:44:31
%S A166130 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A166130 1449027061218,47817893020194,1577990469665841,52073685498954240,
%U A166130 1718431621464879552,56708243508320883072,1871372035773924450624,61755277180517572075776
%N A166130 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166130 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A166130 Computed with Magma using commands similar to those used to compute A154638.
%H A166130 G. C. Greubel, <a href="/A166130/b166130.txt">Table of n, a(n) for n = 0..500</a>
%H A166130 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (32,32,32,32,32,32,32,32,32,-528).
%F A166130 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)/(528*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%p A166130 seq(coeff(series((1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020
%t A166130 CoefficientList[Series[(1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11), {t,0,30}], t] (* _G. C. Greubel_, Apr 26 2016 *)
%t A166130 coxG[{528, 10, -32}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166130 (Sage)
%o A166130 def A166130_list(prec):
%o A166130     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166130     return P( (1+t)*(1-t^10)/(1-33*t+560*t^10-528*t^11) ).list()
%o A166130 A166130_list(30) # _G. C. Greubel_, Mar 11 2020
%Y A166130 Cf. A154638, A170753.
%K A166130 nonn
%O A166130 0,2
%A A166130 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009