cp's OEIS Frontend

A170699 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170699 #12 Nov 21 2016 10:46:24
%S A170699 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A170699 125563633938,2134581776946,36287890208082,616894133537394,
%U A170699 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A170699 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170699 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A170699 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170699 About the initial comment, first disagreement is at index 50 and the difference is 153.  - _Vincenzo Librandi_, Dec 08 2012
%H A170699 Vincenzo Librandi, <a href="/A170699/b170699.txt">Table of n, a(n) for n = 0..200</a>
%H A170699 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A170699 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 A170699 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 A170699 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 A170699 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 A170699 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 A170699 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 A170699 2*t + 1)/(136*t^50 - 16*t^49 - 16*t^48 - 16*t^47 - 16*t^46 - 16*t^45 -
%F A170699 16*t^44 - 16*t^43 - 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 -
%F A170699 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 -
%F A170699 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 -
%F A170699 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 -
%F A170699 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 -
%F A170699 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 -
%F A170699 16*t + 1).
%t A170699 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-16 t^Range[49]] + 136 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170699 nonn
%O A170699 0,2
%A A170699 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009