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A168724 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168724 #13 Nov 18 2018 20:13:57
%S A168724 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A168724 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A168724 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A168724 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168724 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A168724 First disagreement at index 17: a(17) = 18889617541497286590540479431, A170766(17) = 18889617541497286590540480512. - _Klaus Brockhaus_, Mar 28 2011
%C A168724 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168724 G. C. Greubel, <a href="/A168724/b168724.txt">Table of n, a(n) for n = 0..500</a>
%H A168724 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A168724 G.f.: (t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*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).
%t A168724 CoefficientList[Series[(t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*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), {t,0,50}], t] (* _G. C. Greubel_, Aug 06 2016 *)
%t A168724 coxG[{17,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 18 2018 *)
%Y A168724 Cf. A170766 (G.f.: (1+x)/(1-46*x)).
%K A168724 nonn
%O A168724 0,2
%A A168724 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009