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A166129 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166129 #19 Sep 12 2024 17:49:35
%S A166129 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A166129 1133871366144,36283883716608,1161084278930928,37154696925772800,
%U A166129 1188950301624189456,38046409651956777984,1217485108862063788032,38959523483568341778432
%N A166129 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166129 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A166129 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166129 G. C. Greubel, <a href="/A166129/b166129.txt">Table of n, a(n) for n = 0..500</a>
%H A166129 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F A166129 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)/(496*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%p A166129 seq(coeff(series((1+t)*(1-t^10)/(1-32*t+527*t^10-496*t^11), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Mar 11 2020
%t A166129 CoefficientList[Series[(1+t)*(1-t^10)/(1 -32*t +527*t^10 -496*t^11), {t, 0, 30}], t] (* _G. C. Greubel_, Apr 26 2016 *)
%t A166129 coxG[{496, 10, -31}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166129 (Sage)
%o A166129 def A166129_list(prec):
%o A166129     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166129     return P( (1+t)*(1-t^10)/(1-32*t+527*t^10-496*t^11) ).list()
%o A166129 A166129_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166129 nonn
%O A166129 0,2
%A A166129 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009