cp's OEIS Frontend

A168727 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168727 #11 Nov 24 2016 13:16:07
%S A168727 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A168727 33911153642450,1661646528480050,81420679895522450,
%U A168727 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A168727 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168727 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A168727 First disagreement at index 17: a(17) = 55221383712196032315264958825, A170769(17) = 55221383712196032315264960050. - _Klaus Brockhaus_, Mar 27 2011
%C A168727 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168727 G. C. Greubel, <a href="/A168727/b168727.txt">Table of n, a(n) for n = 0..500</a>
%H A168727 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).
%F A168727 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)/(1176*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
%t A168727 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)/(1176*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 06 2016 *)
%Y A168727 Cf. A170769 (G.f.: (1+x)/(1-49*x)).
%K A168727 nonn
%O A168727 0,2
%A A168727 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009