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A168803 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168803 #14 Dec 11 2016 16:55:33
%S A168803 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A168803 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A168803 10614443496164071230,307818861388758065670,8926746980273983904430
%N A168803 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168803 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A168803 First disagreement at index 19: a(19) = 6313718530955163609909154395, A170749(19) = 6313718530955163609909154830. - _Klaus Brockhaus_, Apr 01 2011
%C A168803 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168803 G. C. Greubel, <a href="/A168803/b168803.txt">Table of n, a(n) for n = 0..500</a>
%H A168803 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A168803 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)/(406*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%t A168803 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)/(406*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1), {t, 0, 500}], t] (* _G. C. Greubel_, Aug 16 2016 *)
%t A168803 coxG[{19,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 11 2016 *)
%Y A168803 Cf. A170749 (G.f.: (1+x)/(1-29*x)).
%K A168803 nonn
%O A168803 0,2
%A A168803 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009