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A168813 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168813 #14 May 20 2021 16:04:02
%S A168813 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A168813 5489240267160,214080370419240,8349134446350360,325616243407664040,
%U A168813 12699033492898897560,495262306223057004840,19315229942699223188760
%N A168813 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168813 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A168813 First disagreement at index 19: a(19) = 1742701150080853310128096802460, A170759(19) = 1742701150080853310128096803240. - _Klaus Brockhaus_, Apr 01 2011
%C A168813 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168813 G. C. Greubel, <a href="/A168813/b168813.txt">Table of n, a(n) for n = 0..500</a>
%H A168813 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).
%F A168813 G.f.: (t^19 + 2*t^18 + 2*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)/(741*t^19 - 38*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
%t A168813 CoefficientList[Series[(t^19 + 2*t^18 + 2*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)/(741*t^19 - 38*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 17 2016 *)
%t A168813 coxG[{19,741,-38}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 20 2021 *)
%Y A168813 Cf. A170759 (G.f.: (1+x)/(1-39*x)).
%K A168813 nonn
%O A168813 0,2
%A A168813 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009