cp's OEIS Frontend

A169532 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169532 #9 Nov 26 2016 07:40:26
%S A169532 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A169532 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A169532 9304309958718547968,353563778431304822784,13435423580389583265792
%N A169532 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169532 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A169532 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169532 <a href="/index/Rec#order_34">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, 37, -703).
%F A169532 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169532 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169532 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169532 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A169532 2*t + 1)/(703*t^34 - 37*t^33 - 37*t^32 - 37*t^31 - 37*t^30 - 37*t^29 -
%F A169532 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 -
%F A169532 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 -
%F A169532 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 -
%F A169532 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1)
%t A169532 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-37 t^Range[33]]+703t^34+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Aug 22 2011 *)
%K A169532 nonn
%O A169532 0,2
%A A169532 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009