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A168719 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168719 #13 Apr 10 2018 15:05:34
%S A168719 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A168719 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A168719 23113819332082434522,947666592615379815402,38854330297230572431482
%N A168719 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168719 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A168719 First disagreement at index 17: a(17) = 2677879298415428282550170061, A170761(17) = 2677879298415428282550170922. - _Klaus Brockhaus_, Mar 28 2011
%C A168719 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168719 G. C. Greubel, <a href="/A168719/b168719.txt">Table of n, a(n) for n = 0..500</a>
%H A168719 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A168719 G.f.: (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)/(820*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).
%t A168719 CoefficientList[Series[(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)/(820*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 05 2016 *)
%t A168719 coxG[{17,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 10 2018 *)
%Y A168719 Cf. A170761 (G.f.: (1+x)/(1-41*x)).
%K A168719 nonn
%O A168719 0,2
%A A168719 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009