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%I #11 Mar 18 2018 18:01:38
%S 5,22,57,122,223,366,563,820,1143,1544,2029,2604,3281,4066,4965,5990,
%T 7147,8442,9887,11488,13251,15188,17305,19608,22109,24814,27729,30866,
%U 34231,37830,41675,45772,50127,54752,59653,64836,70313,76090,82173,88574
%N Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
%C Row 4 of A208945.
%H R. H. Hardin, <a href="/A208946/b208946.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) - 3*a(n-4) + 3*a(n-5) - a(n-6).
%F Empirical g.f.: x*(5 + 7*x + 6*x^2 + 7*x^3 - x^4) / ((1 - x)^4*(1 + x + x^2)). - _Colin Barker_, Mar 07 2018
%e Some solutions for n=5:
%e -5 -3 -3 -3 -5 -3 -5 -4 -3 -4 -4 -4 -4 -4 -5 -3
%e 2 0 -3 3 5 4 -5 2 5 1 0 1 0 -3 1 0
%e 4 2 1 -1 0 -2 5 1 -2 -1 -1 -2 3 3 2 5
%e -1 1 5 1 0 1 5 1 0 4 5 5 1 4 2 -2
%Y Cf. A208945.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 03 2012