cp's OEIS Frontend

A170696 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170696 #12 Nov 21 2016 10:43:35
%S A170696 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A170696 309915701760,4338819824640,60743477544960,850408685629440,
%U A170696 11905721598812160,166680102383370240,2333521433367183360
%N A170696 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170696 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A170696 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170696 About the initial comment, first disagreement is at index 50 and the difference is 105.  - _Vincenzo Librandi_, Dec 08 2012
%H A170696 Vincenzo Librandi, <a href="/A170696/b170696.txt">Table of n, a(n) for n = 0..200</a>
%H A170696 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A170696 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 A170696 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 A170696 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 A170696 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 A170696 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 A170696 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 A170696 2*t + 1)/(91*t^50 - 13*t^49 - 13*t^48 - 13*t^47 - 13*t^46 - 13*t^45 -
%F A170696 13*t^44 - 13*t^43 - 13*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 -
%F A170696 13*t^37 - 13*t^36 - 13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 -
%F A170696 13*t^30 - 13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 -
%F A170696 13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 -
%F A170696 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 -
%F A170696 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 -
%F A170696 13*t + 1).
%t A170696 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-13 t^Range[49]] + 91 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170696 nonn
%O A170696 0,2
%A A170696 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009