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A170720 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170720 #16 Jul 26 2018 15:24:21
%S A170720 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A170720 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A170720 9304309958718547968,353563778431304822784,13435423580389583265792
%N A170720 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170720 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A170720 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170720 About the initial comment, first disagreement is at index 50 and the difference is 741.  - _Vincenzo Librandi_, Dec 06 2012
%H A170720 Vincenzo Librandi, <a href="/A170720/b170720.txt">Table of n, a(n) for n = 0..200</a>
%H A170720 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A170720 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 A170720 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 A170720 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 A170720 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 A170720 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 A170720 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 A170720 2*t + 1)/(703*t^50 - 37*t^49 - 37*t^48 - 37*t^47 - 37*t^46 - 37*t^45 -
%F A170720 37*t^44 - 37*t^43 - 37*t^42 - 37*t^41 - 37*t^40 - 37*t^39 - 37*t^38 -
%F A170720 37*t^37 - 37*t^36 - 37*t^35 - 37*t^34 - 37*t^33 - 37*t^32 - 37*t^31 -
%F A170720 37*t^30 - 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 -
%F A170720 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 -
%F A170720 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 -
%F A170720 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 -
%F A170720 37*t + 1)
%t A170720 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-37  t^Range[49]] + 703 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170720 coxG[{50,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 26 2018 *)
%K A170720 nonn
%O A170720 0,2
%A A170720 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009