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%I #13 Jul 08 2018 21:31:06
%S 15,238,1373,5032,14037,32802,67681,127310,222965,368920,582789,
%T 885874,1303543,1865552,2606403,3565722,4788571,6325826,8234535,
%U 10578240,13427355,16859514,20959913,25821668,31546173,38243442,46032457,55041546
%N Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
%C Row 6 of A209115.
%H R. H. Hardin, <a href="/A209118/b209118.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 5*a(n-4) + 7*a(n-5) - 8*a(n-6) + 7*a(n-7) - 5*a(n-8) + 5*a(n-9) - 6*a(n-10) + 4*a(n-11) - a(n-12) for n > 13.
%F Empirical g.f.: x*(15 + 178*x + 511*x^2 + 893*x^3 + 1032*x^4 + 1066*x^5 + 854*x^6 + 561*x^7 + 155*x^8 + 26*x^9 - 23*x^10 + 16*x^11 - 4*x^12) / ((1 - x)^6*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Jul 08 2018
%e Some solutions for n=6:
%e -6 -4 -6 -5 -5 -6 -4 -5 -6 -5 -5 -3 -6 -5 -6 -6
%e 1 0 -1 4 -2 0 3 3 2 -4 -4 -3 4 -2 -5 3
%e 5 -2 -5 -5 -1 2 -2 -5 -3 5 2 2 2 0 2 3
%e -3 -2 2 4 3 -2 0 4 6 -3 0 -2 -2 0 6 -1
%e 2 5 5 -2 -1 2 0 1 1 2 5 5 -1 6 5 5
%e 1 3 5 4 6 4 3 2 0 5 2 1 3 1 -2 -4
%Y Cf. A209115.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 05 2012
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