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%I #10 Nov 25 2016 10:08:05
%S 1,46,2070,93150,4191750,188628750,8488293750,381973218750,
%T 17188794843750,773495767968750,34807309558593750,1566328930136718750,
%U 70484801856152343750,3171816083526855468750,142731723758708496093750
%N Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
%C The initial terms coincide with those of A170765, although the two sequences are eventually different.
%C First disagreement at index 22: a(22) = 2400051832222732793623924255371092715, A170765(22) = 2400051832222732793623924255371093750. - Klaus Brockhaus, Apr 10 2011
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).
%F G.f.: (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)/(990*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
%t With[{num=Total[2t^Range[21]]+t^22+1,den=Total[-44 t^Range[21]]+ 990t^22+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 06 2012 *)
%Y Cf. A170765 (G.f.: (1+x)/(1-45*x)).
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009