cp's OEIS Frontend

A170712 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170712 #27 Nov 29 2020 13:29:08
%S A170712 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170712 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170712 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170712 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170712 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170712 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170712 About the initial comment, first disagreement is at index 50 and the difference is 465.  - _Vincenzo Librandi_, Dec 06 2012
%H A170712 Vincenzo Librandi, <a href="/A170712/b170712.txt">Table of n, a(n) for n = 0..200</a>
%H A170712 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A170712 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 A170712 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 A170712 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 A170712 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 A170712 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 A170712 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 A170712 2*t + 1)/(435*t^50 - 29*t^49 - 29*t^48 - 29*t^47 - 29*t^46 - 29*t^45 -
%F A170712 29*t^44 - 29*t^43 - 29*t^42 - 29*t^41 - 29*t^40 - 29*t^39 - 29*t^38 -
%F A170712 29*t^37 - 29*t^36 - 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 - 29*t^31 -
%F A170712 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 -
%F A170712 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 -
%F A170712 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 -
%F A170712 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 -
%F A170712 29*t + 1).
%t A170712 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-29 t^Range[49]] + 435 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170712 coxG[{50,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 29 2020 *)
%K A170712 nonn
%O A170712 0,2
%A A170712 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009