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A168984 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%I A168984 #10 Apr 02 2017 15:33:27
%S A168984 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A168984 209379250944,3768826516992,67838877305856,1221099791505408,
%U A168984 21979796247097344,395636332447752192,7121453984059539456
%N A168984 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
%C A168984 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A168984 First disagreement at index 23: a(23) = 78478142148134257241836486485, A170738(23) = 78478142148134257241836486656. - Klaus Brockhaus, Apr 19 2011
%C A168984 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168984 <a href="/index/Rec#order_23">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, 17, 17, 17, 17, 17, -153).
%F A168984 G.f.: (t^23 + 2*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)/(153*t^23 - 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 - 17*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 A168984 coxG[{23,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 02 2017 *)
%Y A168984 Cf. A170738 (G.f.: (1+x)/(1-18*x)).
%K A168984 nonn
%O A168984 0,2
%A A168984 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009