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A169484 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169484 #11 Nov 26 2016 07:26:22
%S A169484 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A169484 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A169484 9304309958718547968,353563778431304822784,13435423580389583265792
%N A169484 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169484 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A169484 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169484 Vincenzo Librandi, <a href="/A169484/b169484.txt">Table of n, a(n) for n = 0..200</a>
%H A169484 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A169484 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 A169484 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 A169484 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 A169484 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 A169484 1)/(703*t^33 - 37*t^32 - 37*t^31 - 37*t^30 - 37*t^29 - 37*t^28 - 37*t^27
%F A169484 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 -
%F A169484 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 -
%F A169484 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5
%F A169484 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1)
%t A169484 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-37 t^Range[32]]+703t^33+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 28 2014 *)
%K A169484 nonn
%O A169484 0,2
%A A169484 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009