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A168801 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%I A168801 #14 Jun 12 2018 16:03:29
%S A168801 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A168801 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A168801 4202649788315975388,113471544284531335476,3063731695682346057852
%N A168801 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
%C A168801 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A168801 First disagreement at index 19: a(19) = 1628192636085121671330924354, A170747(19) = 1628192636085121671330924732. - _Klaus Brockhaus_, Apr 01 2011
%C A168801 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168801 G. C. Greubel, <a href="/A168801/b168801.txt">Table of n, a(n) for n = 0..500</a>
%H A168801 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A168801 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)/(351*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%t A168801 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)/(351*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 16 2016 *)
%t A168801 coxG[{19,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2018 *)
%Y A168801 Cf. A170747 (G.f.: (1+x)/(1-27*x)).
%K A168801 nonn
%O A168801 0,2
%A A168801 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009