cp's OEIS Frontend

A170717 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170717 #20 Jul 05 2018 11:04:42
%S A170717 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A170717 2316214687500,81067514062500,2837362992187500,99307704726562500,
%U A170717 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500
%N A170717 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170717 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A170717 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170717 About the initial comment, first disagreement is at index 50 and the difference is 630.  - _Vincenzo Librandi_, Dec 06 2012
%H A170717 Vincenzo Librandi, <a href="/A170717/b170717.txt">Table of n, a(n) for n = 0..200</a>
%H A170717 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
%F A170717 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 A170717 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 A170717 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 A170717 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 A170717 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 A170717 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 A170717 2*t + 1)/(595*t^50 - 34*t^49 - 34*t^48 - 34*t^47 - 34*t^46 - 34*t^45 -
%F A170717 34*t^44 - 34*t^43 - 34*t^42 - 34*t^41 - 34*t^40 - 34*t^39 - 34*t^38 -
%F A170717 34*t^37 - 34*t^36 - 34*t^35 - 34*t^34 - 34*t^33 - 34*t^32 - 34*t^31 -
%F A170717 34*t^30 - 34*t^29 - 34*t^28 - 34*t^27 - 34*t^26 - 34*t^25 - 34*t^24 -
%F A170717 34*t^23 - 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 -
%F A170717 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 -
%F A170717 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 -
%F A170717 34*t + 1).
%t A170717 With[{num = Total[2 t^Range[49]]+ t^50 + 1, den = Total[-34  t^Range[49]] + 595 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170717 coxG[{50,595,-34}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 05 2018 *)
%K A170717 nonn
%O A170717 0,2
%A A170717 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009