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A168743 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168743 #15 Nov 24 2016 13:54:51
%S A168743 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A168743 125563633938,2134581776946,36287890208082,616894133537394,
%U A168743 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A168743 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168743 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A168743 First disagreement at index 18: a(18) = 14890324713954061755033, A170737(18) = 14890324713954061755186. - _Klaus Brockhaus_, Mar 27 2011
%C A168743 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168743 G. C. Greubel, <a href="/A168743/b168743.txt">Table of n, a(n) for n = 0..500</a>
%H A168743 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A168743 G.f.: (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)/(136*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%t A168743 With[{num=Total[2t^Range[17]]+t^18+1,den=Total[-16 t^Range[17]]+ 136t^18+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jan 04 2012 *)
%t A168743 CoefficientList[Series[(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)/(136*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)
%Y A168743 Cf. A170737 (G.f.: (1+x)/(1-17*x)).
%K A168743 nonn,easy
%O A168743 0,2
%A A168743 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009