cp's OEIS Frontend

A169557 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169557 #11 Nov 26 2016 09:27:40
%S A169557 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169557 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169557 31139121093750000,467086816406250000,7006302246093750000
%N A169557 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169557 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169557 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169557 Vincenzo Librandi, <a href="/A169557/b169557.txt">Table of n, a(n) for n = 0..200</a>
%H A169557 <a href="/index/Rec#order_35">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, 14, 14, -105).
%F A169557 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169557 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169557 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169557 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
%F A169557 + 2*t^2 + 2*t + 1)/(105*t^35 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 -
%F A169557 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 -
%F A169557 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 -
%F A169557 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 -
%F A169557 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 -
%F A169557 14*t + 1)
%t A169557 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-14 t^Range[34]]+105t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 25 2014 *)
%K A169557 nonn
%O A169557 0,2
%A A169557 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009