cp's OEIS Frontend

A170689 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170689 #10 Nov 21 2016 10:38:50
%S A170689 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828856,
%T A170689 2259801992,15818613944,110730297608,775112083256,5425784582792,
%U A170689 37980492079544,265863444556808,1861044111897656,13027308783283592
%N A170689 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170689 The initial terms coincide with those of A003950, although the two sequences are eventually different.
%C A170689 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170689 About the initial comment, first disagreement is at index 50 and the difference is 28.  - _Vincenzo Librandi_, Dec 09 2012
%H A170689 Vincenzo Librandi, <a href="/A170689/b170689.txt">Table of n, a(n) for n = 0..200</a>
%H A170689 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).
%F A170689 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 A170689 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 A170689 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 A170689 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 A170689 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 A170689 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 A170689 2*t + 1)/(21*t^50 - 6*t^49 - 6*t^48 - 6*t^47 - 6*t^46 - 6*t^45 - 6*t^44
%F A170689 - 6*t^43 - 6*t^42 - 6*t^41 - 6*t^40 - 6*t^39 - 6*t^38 - 6*t^37 - 6*t^36
%F A170689 - 6*t^35 - 6*t^34 - 6*t^33 - 6*t^32 - 6*t^31 - 6*t^30 - 6*t^29 - 6*t^28
%F A170689 - 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20
%F A170689 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12
%F A170689 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 -
%F A170689 6*t^3 - 6*t^2 - 6*t + 1).
%t A170689 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-6 t^Range[49]] + 21 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* _Vincenzo Librandi_, Dec 09 2012 *)
%K A170689 nonn
%O A170689 0,2
%A A170689 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009