cp's OEIS Frontend

A170011 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170011 #10 Aug 18 2020 14:03:09
%S A170011 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A170011 33911153642450,1661646528480050,81420679895522450,
%U A170011 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A170011 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170011 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A170011 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170011 <a href="/index/Rec#order_35">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, 48, 48, 48, 48, 48, 48, 48, 48, -1176).
%F A170011 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170011 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170011 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170011 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
%F A170011 + 2*t^2 + 2*t + 1)/(1176*t^35 - 48*t^34 - 48*t^33 - 48*t^32 - 48*t^31 -
%F A170011 48*t^30 - 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 -
%F A170011 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 -
%F A170011 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 -
%F A170011 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 -
%F A170011 48*t + 1)
%t A170011 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-48 t^Range[34]]+1176t^35+1}, CoefficientList[Series[num/den,{t,0,30}],t]]
%t A170011 coxG[{35,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 18 2020 *)
%K A170011 nonn
%O A170011 0,2
%A A170011 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009