cp's OEIS Frontend

A170721 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170721 #16 Jan 03 2022 16:56:45
%S A170721 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A170721 5489240267160,214080370419240,8349134446350360,325616243407664040,
%U A170721 12699033492898897560,495262306223057004840,19315229942699223188760
%N A170721 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170721 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A170721 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170721 About the initial comment, first disagreement is at index 50 and the difference is 780.  - _Vincenzo Librandi_, Dec 06 2012
%H A170721 Vincenzo Librandi, <a href="/A170721/b170721.txt">Table of n, a(n) for n = 0..200</a>
%H A170721 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).
%F A170721 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 A170721 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 A170721 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 A170721 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 A170721 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 A170721 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 A170721 2*t + 1)/(741*t^50 - 38*t^49 - 38*t^48 - 38*t^47 - 38*t^46 - 38*t^45 -
%F A170721 38*t^44 - 38*t^43 - 38*t^42 - 38*t^41 - 38*t^40 - 38*t^39 - 38*t^38 -
%F A170721 38*t^37 - 38*t^36 - 38*t^35 - 38*t^34 - 38*t^33 - 38*t^32 - 38*t^31 -
%F A170721 38*t^30 - 38*t^29 - 38*t^28 - 38*t^27 - 38*t^26 - 38*t^25 - 38*t^24 -
%F A170721 38*t^23 - 38*t^22 - 38*t^21 - 38*t^20 - 38*t^19 - 38*t^18 - 38*t^17 -
%F A170721 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 -
%F A170721 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 -
%F A170721 38*t + 1)
%t A170721 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-38  t^Range[49]] + 741 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170721 coxG[{50,741,-38}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 03 2022 *)
%K A170721 nonn
%O A170721 0,2
%A A170721 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009