cp's OEIS Frontend

A168808 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168808 #20 Nov 24 2016 16:23:56
%S A168808 1,35,1190,40460,1375640,46771760,1590239840,54068154560,
%T A168808 1838317255040,62502786671360,2125094746826240,72253221392092160,
%U A168808 2456609527331133440,83524723929258536960,2839840613594790256640,96554580862222868725760
%N A168808 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168808 The initial terms coincide with those of A170754, although the two sequences are eventually different.
%C A168808 First disagreement at index 19: a(19) = 129029362371099459501507214765, A170754(19) = 129029362371099459501507215360. - _Klaus Brockhaus_, Apr 01 2011
%C A168808 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168808 Vincenzo Librandi, <a href="/A168808/b168808.txt">Table of n, a(n) for n = 0..200</a>
%H A168808 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).
%F A168808 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)/(561*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
%t A168808 With[{num=Total[2t^Range[18]]+t^19+1,den=Total[-33 t^Range[18]]+ 561t^19+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 11 2012 *)
%Y A168808 Cf. A170754 (G.f.: (1+x)/(1-34*x)).
%K A168808 nonn
%O A168808 0,2
%A A168808 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009