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A170711 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170711 #25 Oct 10 2024 05:10:12
%S A170711 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A170711 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A170711 10614443496164071230,307818861388758065670,8926746980273983904430
%N A170711 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170711 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A170711 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170711 About the initial comment, first disagreement is at index 50 and the difference is 435. - _Vincenzo Librandi_, Dec 06 2012
%H A170711 Vincenzo Librandi, <a href="/A170711/b170711.txt">Table of n, a(n) for n = 0..200</a>
%H A170711 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A170711 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 A170711 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 A170711 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 A170711 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 A170711 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 A170711 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 A170711 2*t + 1)/(406*t^50 - 28*t^49 - 28*t^48 - 28*t^47 - 28*t^46 - 28*t^45 -
%F A170711 28*t^44 - 28*t^43 - 28*t^42 - 28*t^41 - 28*t^40 - 28*t^39 - 28*t^38 -
%F A170711 28*t^37 - 28*t^36 - 28*t^35 - 28*t^34 - 28*t^33 - 28*t^32 - 28*t^31 -
%F A170711 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 -
%F A170711 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 -
%F A170711 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 -
%F A170711 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 -
%F A170711 28*t + 1).
%t A170711 With[{num=Total[2 t^Range[49]] + t^50 + 1, den = Total[-28t^Range[49]] + 406 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170711 coxG[{50,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 02 2017 *)
%K A170711 nonn
%O A170711 0,2
%A A170711 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009