cp's OEIS Frontend

A170731 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170731 #11 Apr 12 2022 11:26:24
%S A170731 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T A170731 33911153642450,1661646528480050,81420679895522450,
%U A170731 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450
%N A170731 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170731 The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C A170731 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170731 About the initial comment, first disagreement is at index 50 and the difference is 1225.  - _Vincenzo Librandi_, Dec 08 2012
%H A170731 Vincenzo Librandi, <a href="/A170731/b170731.txt">Table of n, a(n) for n = 0..200</a>
%H A170731 <a href="/index/Rec#order_50">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, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).
%F A170731 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 A170731 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 A170731 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 A170731 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 A170731 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 A170731 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 A170731 2*t + 1)/(1176*t^50 - 48*t^49 - 48*t^48 - 48*t^47 - 48*t^46 - 48*t^45 -
%F A170731 48*t^44 - 48*t^43 - 48*t^42 - 48*t^41 - 48*t^40 - 48*t^39 - 48*t^38 -
%F A170731 48*t^37 - 48*t^36 - 48*t^35 - 48*t^34 - 48*t^33 - 48*t^32 - 48*t^31 -
%F A170731 48*t^30 - 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 -
%F A170731 48*t^23 - 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 -
%F A170731 48*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 -
%F A170731 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 A170731 48*t + 1)
%t A170731 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-48 t^Range[49]] + 1176t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Libramdi_, Dec 08 2012 *)
%t A170731 coxG[{50,1176,-48}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Apr 12 2022 *)
%K A170731 nonn
%O A170731 0,2
%A A170731 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009