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A166324 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166324 #16 Mar 12 2020 07:24:15
%S A166324 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A166324 28766348771328,1380784741023744,66277667569138536,
%U A166324 3181328043318593280,152703746079289769112,7329779811805778917632,351829430966671148058624
%N A166324 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166324 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A166324 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166324 G. C. Greubel, <a href="/A166324/b166324.txt">Table of n, a(n) for n = 0..500</a>
%H A166324 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (47,47,47,47,47,47,47,47,47,-1128).
%F A166324 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)/(1128*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
%p A166324 seq(coeff(series((1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 12 2020
%t A166324 CoefficientList[Series[(1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11), {t,0,30}], t] (* _G, C, Greubel_, May 09 2016 *)
%t A166324 coxG[{10, 1128, -47}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 12 2020 *)
%o A166324 (Sage)
%o A166324 def A166324_list(prec):
%o A166324     P.<t> = PowerSeriesRing(ZZ, prec)
%o A166324     return P( (1+t)*(1-t^10)/(1-48*t+1175*t^10-1128*t^11) ).list()
%o A166324 A166324_list(30) # _G. C. Greubel_, Mar 12 2020
%K A166324 nonn
%O A166324 0,2
%A A166324 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009