cp's OEIS Frontend

A170722 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170722 #14 Nov 18 2016 17:49:36
%S A170722 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A170722 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A170722 17196646400000000000,687865856000000000000,27514634240000000000000
%N A170722 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170722 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A170722 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170722 About the initial comment, first disagreement is at index 50 and the difference is 820.  - _Vincenzo Librandi_, Dec 06 2012
%H A170722 Vincenzo Librandi, <a href="/A170722/b170722.txt">Table of n, a(n) for n = 0..200</a>
%H A170722 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A170722 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 A170722 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 A170722 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 A170722 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 A170722 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 A170722 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 A170722 2*t + 1)/(780*t^50 - 39*t^49 - 39*t^48 - 39*t^47 - 39*t^46 - 39*t^45 -
%F A170722 39*t^44 - 39*t^43 - 39*t^42 - 39*t^41 - 39*t^40 - 39*t^39 - 39*t^38 -
%F A170722 39*t^37 - 39*t^36 - 39*t^35 - 39*t^34 - 39*t^33 - 39*t^32 - 39*t^31 -
%F A170722 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 -
%F A170722 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 -
%F A170722 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 -
%F A170722 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 -
%F A170722 39*t + 1)
%t A170722 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-39  t^Range[49]] + 780 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%K A170722 nonn
%O A170722 0,2
%A A170722 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009