cp's OEIS Frontend

A170697 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170697 #12 Nov 21 2016 10:44:25
%S A170697 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A170697 615093750000,9226406250000,138396093750000,2075941406250000,
%U A170697 31139121093750000,467086816406250000,7006302246093750000
%N A170697 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170697 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A170697 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170697 About the initial comment, first disagreement is at index 50 and the difference is 120.  - _Vincenzo Librandi_, Dec 08 2012
%H A170697 Vincenzo Librandi, <a href="/A170697/b170697.txt">Table of n, a(n) for n = 0..200</a>
%H A170697 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A170697 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 A170697 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 A170697 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 A170697 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 A170697 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 A170697 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 A170697 2*t + 1)/(105*t^50 - 14*t^49 - 14*t^48 - 14*t^47 - 14*t^46 - 14*t^45 -
%F A170697 14*t^44 - 14*t^43 - 14*t^42 - 14*t^41 - 14*t^40 - 14*t^39 - 14*t^38 -
%F A170697 14*t^37 - 14*t^36 - 14*t^35 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 -
%F A170697 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 -
%F A170697 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 -
%F A170697 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 -
%F A170697 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 -
%F A170697 14*t + 1).
%t A170697 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-14 t^Range[49]] + 105t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170697 nonn
%O A170697 0,2
%A A170697 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009