cp's OEIS Frontend

A169499 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169499 #8 Nov 26 2016 07:31:16
%S A169499 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A169499 292968750,1464843750,7324218750,36621093750,183105468750,
%U A169499 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A169499 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169499 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A169499 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169499 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A169499 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169499 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169499 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169499 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 +
%F A169499 2*t + 1)/(10*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28
%F A169499 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20
%F A169499 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12
%F A169499 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 -
%F A169499 4*t^3 - 4*t^2 - 4*t + 1)
%t A169499 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-4 t^Range[33]]+ 10t^34+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 13 2012 *)
%K A169499 nonn
%O A169499 0,2
%A A169499 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009