cp's OEIS Frontend

A170728 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170728 #12 Nov 18 2016 17:33:52
%S A170728 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170728 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170728 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170728 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170728 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170728 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170728 About the initial comment, first disagreement is at index 50 and the difference is 1081.  - _Vincenzo Librandi_, Dec 08 2012
%H A170728 Vincenzo Librandi, <a href="/A170728/b170728.txt">Table of n, a(n) for n = 0..200</a>
%H A170728 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A170728 G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +
%F A170728 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170728 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170728 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170728 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170728 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 +
%F A170728 2*t + 1)/(1035*t^50 - 45*t^49 - 45*t^48 - 45*t^47 - 45*t^46 - 45*t^45 -
%F A170728 45*t^44 - 45*t^43 - 45*t^42 - 45*t^41 - 45*t^40 - 45*t^39 - 45*t^38 -
%F A170728 45*t^37 - 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 -
%F A170728 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 -
%F A170728 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 -
%F A170728 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 -
%F A170728 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 -
%F A170728 45*t + 1)
%t A170728 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-45 t^Range[49]]+ 1035t^50+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Apr 18 2012 *)
%K A170728 nonn
%O A170728 0,2
%A A170728 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009