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A168792 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168792 #14 Nov 24 2016 16:18:53
%S A168792 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A168792 209379250944,3768826516992,67838877305856,1221099791505408,
%U A168792 21979796247097344,395636332447752192,7121453984059539456
%N A168792 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168792 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A168792 First disagreement at index 19: a(19) = 747581753430634213932885, A170738(19) = 747581753430634213933056. - _Klaus Brockhaus_, Mar 30 2011
%C A168792 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168792 G. C. Greubel, <a href="/A168792/b168792.txt">Table of n, a(n) for n = 0..500</a>
%H A168792 <a href="/index/Rec#order_19">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, -153).
%F A168792 G.f.: (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^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 A168792 coxG[{19,153,-17}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 06 2015 *)
%t A168792 CoefficientList[Series[(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^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, 0, 50}], t] (* _G. C. Greubel_, Aug 15 2016 *)
%Y A168792 Cf. A170738 (G.f.: (1+x)/(1-18*x)).
%K A168792 nonn
%O A168792 0,2
%A A168792 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009