cp's OEIS Frontend

A169451 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169451 #11 Jun 19 2022 18:50:37
%S A169451 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A169451 292968750,1464843750,7324218750,36621093750,183105468750,
%U A169451 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A169451 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169451 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A169451 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169451 <a href="/index/Rec#order_33">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, -10).
%F A169451 G.f. (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A169451 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A169451 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A169451 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 +
%F A169451 1)/(10*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 -
%F A169451 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 -
%F A169451 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 -
%F A169451 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 -
%F A169451 4*t + 1)
%t A169451 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-4 t^Range[32]]+ 10t^33+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 27 2012 *)
%t A169451 coxG[{33,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 19 2022 *)
%K A169451 nonn
%O A169451 0,2
%A A169451 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009