cp's OEIS Frontend

A170059 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170059 #8 Nov 26 2016 09:50:51
%S A170059 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A170059 33911153642450,1661646528480050,81420679895522450,
%U A170059 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A170059 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170059 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A170059 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170059 <a href="/index/Rec#order_36">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, 48, -1176).
%F A170059 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170059 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170059 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170059 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
%F A170059 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^36 - 48*t^35 - 48*t^34 - 48*t^33 -
%F A170059 48*t^32 - 48*t^31 - 48*t^30 - 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 -
%F A170059 48*t^25 - 48*t^24 - 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 -
%F A170059 48*t^18 - 48*t^17 - 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 -
%F A170059 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4
%F A170059 - 48*t^3 - 48*t^2 - 48*t + 1)
%t A170059 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-48 t^Range[35]]+1176t^36+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 16 2014 *)
%K A170059 nonn
%O A170059 0,2
%A A170059 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009