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A166308 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%I A166308 #18 Sep 08 2022 08:45:48
%S A166308 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A166308 20483429889152,942237774900992,43342937645444551,1993775131690399620,
%U A166308 91713656057756096205,4218828178656675254940,194066096218202223884700
%N A166308 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A166308 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A166308 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166308 G. C. Greubel, <a href="/A166308/b166308.txt">Table of n, a(n) for n = 0..500</a>
%H A166308 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A166308 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)/(1035*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%F A166308 G.f.: (1+x)*(1-x^10)/(1 -46*x +1080*x^10 -1035*x^11). - _G. C. Greubel_, Apr 25 2019
%t A166308 CoefficientList[Series[(1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11), {x, 0, 20}], x] (* _G. C. Greubel_, May 09 2016, modified Apr 25 2019 *)
%t A166308 coxG[{10,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 07 2017 *)
%o A166308 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1-46*x+1080*x^10 -1035*x^11)) \\ _G. C. Greubel_, Apr 25 2019
%o A166308 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11) )); // _G. C. Greubel_, Apr 25 2019
%o A166308 (Sage) ((1+x)*(1-x^10)/(1-46*x+1080*x^10-1035*x^11)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A166308 nonn
%O A166308 0,2
%A A166308 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009