cp's OEIS Frontend

A169538 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169538 #8 Nov 26 2016 07:42:01
%S A169538 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A169538 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A169538 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A169538 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169538 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A169538 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169538 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A169538 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 A169538 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 A169538 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 A169538 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 A169538 2*t + 1)/(946*t^34 - 43*t^33 - 43*t^32 - 43*t^31 - 43*t^30 - 43*t^29 -
%F A169538 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 -
%F A169538 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 -
%F A169538 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 -
%F A169538 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)
%t A169538 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-43 t^Range[33]]+946t^34+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Dec 09 2013 *)
%K A169538 nonn
%O A169538 0,2
%A A169538 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009