cp's OEIS Frontend

A170713 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170713 #26 Nov 15 2018 17:01:39
%S A170713 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A170713 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A170713 25205209081233592352,781361481518241362912,24222205927065482250272
%N A170713 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170713 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A170713 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170713 About the initial comment, first disagreement is at index 50 and the difference is 496.  - _Vincenzo Librandi_, Dec 06 2012
%H A170713 Vincenzo Librandi, <a href="/A170713/b170713.txt">Table of n, a(n) for n = 0..200</a>
%H A170713 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A170713 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 A170713 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 A170713 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 A170713 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 A170713 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 A170713 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 A170713 2*t + 1)/(465*t^50 - 30*t^49 - 30*t^48 - 30*t^47 - 30*t^46 - 30*t^45 -
%F A170713 30*t^44 - 30*t^43 - 30*t^42 - 30*t^41 - 30*t^40 - 30*t^39 - 30*t^38 -
%F A170713 30*t^37 - 30*t^36 - 30*t^35 - 30*t^34 - 30*t^33 - 30*t^32 - 30*t^31 -
%F A170713 30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 - 30*t^24 -
%F A170713 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 -
%F A170713 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 -
%F A170713 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 -
%F A170713 30*t + 1).
%t A170713 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-30 t^Range[49]] + 465 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170713 coxG[{50,465,-30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 15 2018 *)
%K A170713 nonn
%O A170713 0,2
%A A170713 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009