cp's OEIS Frontend

A170700 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170700 #12 Nov 21 2016 10:47:08
%S A170700 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T A170700 209379250944,3768826516992,67838877305856,1221099791505408,
%U A170700 21979796247097344,395636332447752192,7121453984059539456
%N A170700 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170700 The initial terms coincide with those of A170738, although the two sequences are eventually different.
%C A170700 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170700 About the initial comment, first disagreement is at index 50 and the difference is 171.  - _Vincenzo Librandi_, Dec 08 2012
%H A170700 Vincenzo Librandi, <a href="/A170700/b170700.txt">Table of n, a(n) for n = 0..200</a>
%H A170700 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).
%F A170700 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 A170700 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 A170700 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 A170700 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 A170700 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 A170700 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 A170700 2*t + 1)/(153*t^50 - 17*t^49 - 17*t^48 - 17*t^47 - 17*t^46 - 17*t^45 -
%F A170700 17*t^44 - 17*t^43 - 17*t^42 - 17*t^41 - 17*t^40 - 17*t^39 - 17*t^38 -
%F A170700 17*t^37 - 17*t^36 - 17*t^35 - 17*t^34 - 17*t^33 - 17*t^32 - 17*t^31 -
%F A170700 17*t^30 - 17*t^29 - 17*t^28 - 17*t^27 - 17*t^26 - 17*t^25 - 17*t^24 -
%F A170700 17*t^23 - 17*t^22 - 17*t^21 - 17*t^20 - 17*t^19 - 17*t^18 - 17*t^17 -
%F A170700 17*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 -
%F A170700 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 -
%F A170700 17*t + 1).
%t A170700 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-17 t^Range[49]] + 153t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170700 nonn
%O A170700 0,2
%A A170700 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009