cp's OEIS Frontend

A170725 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170725 #18 May 09 2019 01:45:09
%S A170725 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170725 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170725 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170725 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170725 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170725 The first disagreement is at index 50 and the difference is 946.  - _Vincenzo Librandi_, Dec 07 2012
%H A170725 Georg Fischer, <a href="/A170725/b170725.txt">Table of n, a(n) for n = 0..200</a> (first 50 terms from Vincenzo Librandi)
%H A170725 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A170725 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 A170725 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 A170725 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 A170725 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 A170725 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 A170725 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 A170725 2*t + 1)/(903*t^50 - 42*t^49 - 42*t^48 - 42*t^47 - 42*t^46 - 42*t^45 -
%F A170725 42*t^44 - 42*t^43 - 42*t^42 - 42*t^41 - 42*t^40 - 42*t^39 - 42*t^38 -
%F A170725 42*t^37 - 42*t^36 - 42*t^35 - 42*t^34 - 42*t^33 - 42*t^32 - 42*t^31 -
%F A170725 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 -
%F A170725 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 -
%F A170725 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 -
%F A170725 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 -
%F A170725 42*t + 1)
%t A170725 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-42 t^Range[49]]+ 903t^50+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 02 2012 *)
%K A170725 nonn,easy
%O A170725 0,2
%A A170725 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009