%I #13 Sep 08 2022 08:45:47
%S 1,10,90,810,7290,65610,590490,5314410,47829645,430466400,3874194000,
%T 34867713600,313809130800,2824279552800,25418492355600,
%U 228766218624000,2058894054430380,18530029271219040,166770108473225760
%N Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.
%C The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A164779/b164779.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, 8, 8, 8, 8, -36).
%F G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/( 36*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%F G.f.: (1+x)*(1-x^8)/(1 -9*x +44*x^8 -36*x^9). - _G. C. Greubel_, Apr 26 2019
%t coxG[{8,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 13 2017 *)
%t CoefficientList[Series[(1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9), {x,0,20}], x] (* _G. C. Greubel_, Apr 26 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)) \\ _G. C. Greubel_, Apr 26 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9) )); // _G. C. Greubel_, Apr 26 2019
%o (Sage) ((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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