%I #13 Jul 08 2018 07:59:47
%S 8,70,276,766,1722,3378,6006,9928,15514,23180,33380,46624,63464,84498,
%T 110368,141766,179426,224134,276714,338040,409034,490664,583936,
%U 689912,809696,944438,1095332,1263622,1450594,1657586,1885974,2137184,2412690
%N Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2.
%C Row 5 of A209073.
%H R. H. Hardin, <a href="/A209074/b209074.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-6) - 2*a(n-7) + 3*a(n-8) - 3*a(n-9) + a(n-10).
%F Empirical g.f.: 2*x*(4 + 23*x + 45*x^2 + 66*x^3 + 64*x^4 + 49*x^5 + 21*x^6 + 4*x^7) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jul 08 2018
%e Some solutions for n=6:
%e -6 -3 -6 -3 -4 -4 -6 -2 -3 -3 -5 -4 -6 -3 -4 -3
%e 3 0 5 -1 5 -1 6 -2 1 5 -4 5 3 -1 1 1
%e 3 -1 0 -3 -1 6 2 0 2 -2 6 4 6 2 6 0
%e 4 0 -3 3 0 0 -3 2 1 0 6 -3 -2 4 -2 -1
%e -4 4 4 4 0 -1 1 2 -1 0 -3 -2 -1 -2 -1 3
%Y Cf. A209073.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 04 2012
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