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A168739 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168739 #20 Nov 24 2016 13:53:10
%S A168739 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T A168739 148462991222,1930018885886,25090245516518,326173191714734,
%U A168739 4240251492291542,55123269399790046,716602502197270598
%N A168739 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168739 The initial terms coincide with those of A170733, although the two sequences are eventually different.
%C A168739 First disagreement at index 18: a(18) = 121105822871338730971, A170733(18) = 121105822871338731062. - _Klaus Brockhaus_, Mar 27 2011
%C A168739 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168739 G. C. Greubel, <a href="/A168739/b168739.txt">Table of n, a(n) for n = 0..500</a>
%H A168739 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
%F A168739 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)/(78*t^18 - 12*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
%t A168739 With[{num=Total[2t^Range[17]]+t^18+1,den=Total[-12 t^Range[17]]+ 78t^18+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jun 27 2011 *)
%t A168739 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)/(78*t^18 - 12*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1), {t, 0, 500}], t] (* _G. C. Greubel_, Aug 08 2016 *)
%Y A168739 Cf. A170733 (G.f.: (1+x)/(1-13*x)).
%K A168739 nonn,easy
%O A168739 0,2
%A A168739 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009