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%I A170687 #13 Nov 21 2016 10:37:32
%S A170687 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170687 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170687 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170687 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170687 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170687 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170687 About the initial comment, first disagreement is at index 50 and the difference is 15. - _Vincenzo Librandi_, Dec 09 2012
%H A170687 Vincenzo Librandi, <a href="/A170687/b170687.txt">Table of n, a(n) for n = 0..200</a>
%H A170687 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A170687 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 A170687 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 A170687 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 A170687 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 A170687 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 A170687 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 A170687 2*t + 1)/(10*t^50 - 4*t^49 - 4*t^48 - 4*t^47 - 4*t^46 - 4*t^45 - 4*t^44
%F A170687 - 4*t^43 - 4*t^42 - 4*t^41 - 4*t^40 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36
%F A170687 - 4*t^35 - 4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28
%F A170687 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20
%F A170687 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12
%F A170687 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 -
%F A170687 4*t^3 - 4*t^2 - 4*t + 1)
%t A170687 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-4 t^Range[49]]+10t^50+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 26 2012 *)
%K A170687 nonn
%O A170687 0,2
%A A170687 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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