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A168840 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168840 #10 Jan 20 2020 13:51:36
%S A168840 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A168840 209379250944,3768826516992,67838877305856,1221099791505408,
%U A168840 21979796247097344,395636332447752192,7121453984059539456
%N A168840 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168840 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A168840 First disagreement at index 20: a(20) = 13456471561751415850794837, A170738(20) = 13456471561751415850795008. - Klaus Brockhaus, Apr 02 2011
%C A168840 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168840 <a href="/index/Rec#order_20">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, -153).
%F A168840 G.f.: (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^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 A168840 coxG[{20,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 20 2020 *)
%Y A168840 Cf. A170738 (G.f.: (1+x)/(1-18*x)).
%K A168840 nonn
%O A168840 0,2
%A A168840 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009