cp's OEIS Frontend

A169207 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169207 #13 May 10 2018 02:17:13
%S A169207 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A169207 33911153642450,1661646528480050,81420679895522450,
%U A169207 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A169207 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169207 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A169207 First disagreement at index 27: a(27) = 4406239354486159759219686834395640905665558825, A170769(27) = 4406239354486159759219686834395640905665560050. - _Klaus Brockhaus_, May 07 2011
%C A169207 Computed with Magma using commands similar to those used to compute A154638.
%H A169207 <a href="/index/Rec#order_27">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, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).
%F A169207 G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*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)/(1176*t^27 - 48*t^26 - 48*t^25 - 48*t^24 - 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*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 A169207 With[{num=Total[2t^Range[26]]+t^27+1,den=Total[-48 t^Range[26]]+ 1176t^27+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 24 2011 *)
%Y A169207 Cf. A170769 (G.f.: (1+x)/(1-49*x)).
%K A169207 nonn
%O A169207 0,2
%A A169207 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009