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A166128 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166128 #19 Mar 11 2020 17:35:17
%S A166128 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A166128 27292513198112,846067909140976,26228105183354880,813071260683525120,
%U A166128 25205209081174517760,781361481515952460800,24222205926980341002240
%N A166128 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166128 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A166128 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166128 G. C. Greubel, <a href="/A166128/b166128.txt">Table of n, a(n) for n = 0..500</a>
%H A166128 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A166128 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)/(465*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%p A166128 seq(coeff(series((1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Mar 11 2020
%t A166128 CoefficientList[Series[(1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11), {t, 0, 30}], t] (* _G. C. Greubel_, Apr 26 2016 *)
%t A166128 coxG[{465, 10, -30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)
%o A166128 (Sage)
%o A166128 def A166128_list(prec):
%o A166128     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166128 return P( (1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11) ).list() A166128_list(30) # _G. C. Greubel_, Mar 11 2020
%K A166128 nonn
%O A166128 0,2
%A A166128 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009