cp's OEIS Frontend

A168865 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168865 #10 Nov 24 2016 18:41:07
%S A168865 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A168865 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A168865 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A168865 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168865 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A168865 First disagreement at index 20: a(20) = 477917939121058331055964966178962, A170763(20) = 477917939121058331055964966179908. - Klaus Brockhaus, Apr 04 2011
%C A168865 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168865 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A168865 G.f.: (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)/(903*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%t A168865 With[{num=Total[2t^Range[19]]+t^20+1,den=Total[-42 t^Range[19]]+903t^20+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 17 2014 *)
%Y A168865 Cf. A170763 (G.f.: (1+x)/(1-43*x)).
%K A168865 nonn
%O A168865 0,2
%A A168865 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009