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%I #11 Nov 24 2016 18:35:00
%S 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T 832102905942,17474161024782,366957381520422,7706105011928862,
%U 161828205250506102,3398392310260628142,71366238515473190982
%N Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C First disagreement at index 20: a(20) = 291466926087282574762776951, A170741(20) = 291466926087282574762777182. - Klaus Brockhaus, Apr 02 2011
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F G.f.: (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)/(210*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%t With[{num=Total[2t^Range[19]]+t^20+1,den=Total[-20 t^Range[19]]+ 210t^20+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 21 2011 *)
%Y Cf. A170741 (G.f.: (1+x)/(1-21*x)).
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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