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A168744 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168744 #17 Dec 02 2024 15:34:58
%S A168744 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A168744 209379250944,3768826516992,67838877305856,1221099791505408,
%U A168744 21979796247097344,395636332447752192,7121453984059539456
%N A168744 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168744 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A168744 First disagreement at index 18: a(18) = 41532319635035234107221, A170738(18) = 41532319635035234107392. - _Klaus Brockhaus_, Mar 27 2011
%C A168744 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168744 G. C. Greubel, <a href="/A168744/b168744.txt">Table of n, a(n) for n = 0..500</a>
%H A168744 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).
%F A168744 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)/(153*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 -17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5- 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
%t A168744 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)/(153*t^18 - 17*t^17 - 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 10 2016 *)
%t A168744 coxG[{18,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 02 2024 *)
%Y A168744 Cf. A170738 (G.f.: (1+x)/(1-18*x)).
%K A168744 nonn,easy
%O A168744 0,2
%A A168744 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009