cp's OEIS Frontend

A169461 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169461 #9 Nov 26 2016 07:20:08
%S A169461 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169461 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169461 31139121093750000,467086816406250000,7006302246093750000
%N A169461 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169461 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169461 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169461 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A169461 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 A169461 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 A169461 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 A169461 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 A169461 1)/(105*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27
%F A169461 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 -
%F A169461 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 -
%F A169461 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5
%F A169461 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)
%t A169461 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-14 t^Range[32]]+ 105t^33+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 03 2012 *)
%K A169461 nonn
%O A169461 0,2
%A A169461 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009