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A168748 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168748 #15 Nov 24 2016 13:56:31
%S A168748 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A168748 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A168748 295665060514131968,6504631331310903296,143101889288839872512
%N A168748 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168748 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A168748 First disagreement at index 18: a(18) = 1523748917147566962507523, A170742(18) = 1523748917147566962507776. - _Klaus Brockhaus_, Mar 26 2011
%C A168748 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168748 G. C. Greubel, <a href="/A168748/b168748.txt">Table of n, a(n) for n = 0..500</a>
%H A168748 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A168748 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)/(231*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
%t A168748 With[{num=Total[2t^Range[17]]+t^18+1,den=Total[-21 t^Range[17]]+231t^18+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 18 2013 *)
%t A168748 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)/(231*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)
%Y A168748 Cf. A170742 (G.f.: (1+x)/(1-22*x)).
%K A168748 nonn,easy
%O A168748 0,2
%A A168748 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009