cp's OEIS Frontend

A168909 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

%I A168909 #11 Nov 25 2016 09:42:49
%S A168909 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A168909 5489240267160,214080370419240,8349134446350360,325616243407664040,
%U A168909 12699033492898897560,495262306223057004840,19315229942699223188760
%N A168909 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
%C A168909 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A168909 First disagreement at index 21: a(21) = 2650648449272977884704835237727260, A170759(21) = 2650648449272977884704835237728040. - Klaus Brockhaus, Apr 05 2011
%C A168909 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168909 <a href="/index/Rec#order_21">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, 38, 38, -741).
%F A168909 G.f.: (t^21 + 2*t^20 + 2*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^21 - 38*t^20 - 38*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 A168909 With[{num=Total[2t^Range[20]]+t^21+1,den=Total[-38 t^Range[20]]+ 741t^21+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Nov 05 2011 *)
%Y A168909 Cf. A170759 (G.f.: (1+x)/(1-39*x)).
%K A168909 nonn
%O A168909 0,2
%A A168909 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009