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%I #12 Jul 07 2018 08:51:10
%S 20,264,1464,5238,14430,33468,68722,128844,225126,371858,586668,
%T 890880,1309872,1873416,2616036,3577366,4802490,6342300,8253854,
%U 10600716,13453314,16889298,20993880,25860192,31589644,38292264,46087056,55102358
%N Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
%C Row 6 of A208945.
%H R. H. Hardin, <a href="/A208948/b208948.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 10*a(n-6) + 5*a(n-7) - a(n-8).
%F Empirical g.f.: 2*x*(10 + 82*x + 172*x^2 + 169*x^3 + 88*x^4 + 7*x^5) / ((1 - x)^6*(1 + x + x^2)). - _Colin Barker_, Jul 07 2018
%e Some solutions for n=5:
%e -3 -4 -5 -2 -4 -2 -5 -4 -5 -5 -5 -4 -5 -3 -5 -4
%e -1 4 -2 -1 -1 0 -2 1 -1 5 -4 -3 0 5 2 2
%e -2 0 0 -2 0 2 -3 2 3 1 3 3 3 -2 3 0
%e 2 -1 0 3 4 1 3 -2 -5 2 1 1 -3 -2 5 -4
%e 1 3 3 3 -1 0 3 4 3 -4 1 1 4 -1 -3 4
%e 3 -2 4 -1 2 -1 4 -1 5 1 4 2 1 3 -2 2
%Y Cf. A208945.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 03 2012
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