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%I #11 Nov 25 2016 14:01:04
%S 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U 10614443496164071230,307818861388758065670,8926746980273983904430
%N Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C First disagreement at index 27: a(27) = 3158415047555715036977934578782667751195, A170749(27) = 3158415047555715036977934578782667751630. - Klaus Brockhaus, May 07 2011
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(406*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%t With[{num=Total[2t^Range[26]]+t^27+1,den=Total[-28 t^Range[26]]+ 406t^27+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 21 2011 *)
%Y Cf. A170749 (G.f.: (1+x)/(1-29*x)).
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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