cp's OEIS Frontend

A169463 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169463 #12 Nov 26 2016 07:20:39
%S A169463 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A169463 125563633938,2134581776946,36287890208082,616894133537394,
%U A169463 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A169463 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169463 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A169463 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169463 Vincenzo Librandi, <a href="/A169463/b169463.txt">Table of n, a(n) for n = 0..300</a>
%H A169463 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A169463 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 A169463 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 A169463 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 A169463 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 A169463 1)/(136*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27
%F A169463 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 -
%F A169463 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 -
%F A169463 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5
%F A169463 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
%t A169463 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-16 t^Range[32]]+136t^33+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 09 2014 *)
%K A169463 nonn
%O A169463 0,2
%A A169463 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009