cp's OEIS Frontend

A170716 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170716 #18 Nov 18 2016 18:07:38
%S A170716 1,35,1190,40460,1375640,46771760,1590239840,54068154560,
%T A170716 1838317255040,62502786671360,2125094746826240,72253221392092160,
%U A170716 2456609527331133440,83524723929258536960,2839840613594790256640,96554580862222868725760
%N A170716 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170716 The initial terms coincide with those of A170754, although the two sequences are eventually different.
%C A170716 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170716 About the initial comment, first disagreement is at index 50 and the difference is 595.  - _Vincenzo Librandi_, Dec 06 2012
%H A170716 Vincenzo Librandi, <a href="/A170716/b170716.txt">Table of n, a(n) for n = 0..200</a>
%H A170716 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).
%F A170716 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 A170716 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 A170716 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 A170716 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 A170716 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 A170716 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 A170716 2*t + 1)/(561*t^50 - 33*t^49 - 33*t^48 - 33*t^47 - 33*t^46 - 33*t^45 -
%F A170716 33*t^44 - 33*t^43 - 33*t^42 - 33*t^41 - 33*t^40 - 33*t^39 - 33*t^38 -
%F A170716 33*t^37 - 33*t^36 - 33*t^35 - 33*t^34 - 33*t^33 - 33*t^32 - 33*t^31 -
%F A170716 33*t^30 - 33*t^29 - 33*t^28 - 33*t^27 - 33*t^26 - 33*t^25 - 33*t^24 -
%F A170716 33*t^23 - 33*t^22 - 33*t^21 - 33*t^20 - 33*t^19 - 33*t^18 - 33*t^17 -
%F A170716 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 -
%F A170716 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 -
%F A170716 33*t + 1).
%t A170716 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-33 t^Range[49]]+ 561t^50+ 1},CoefficientList[Series[num/den,{t,0,40}],t]] (* _Harvey P. Dale_, Sep 10 2012 *)
%K A170716 nonn
%O A170716 0,2
%A A170716 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009