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%I #9 Mar 18 2018 17:45:45
%S 4,33,144,471,1237,2798,5648,10483,18174,29863,46918,71037,104183,
%T 148732,207352,283199,379766,501099,651612,836369,1060813,1331122,
%U 1653894,2036531,2486878,3013693,3626176,4334533,5149447,6082684,7146500,8354355
%N Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.
%C Row 6 of A209032.
%H R. H. Hardin, <a href="/A209034/b209034.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 3*a(n-5) - 3*a(n-6) - 2*a(n-7) + a(n-8) + 4*a(n-9) + 4*a(n-10) + a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) + 2*a(n-16) + 2*a(n-17) - a(n-19).
%e Some solutions for n=6:
%e -4 -2 -4 -5 -4 -3 -1 -2 -3 -2 -3 -4 -4 -6 -3 -3
%e -2 -2 -2 -1 -1 1 -1 -1 0 -2 -2 -2 -3 0 -2 -2
%e 3 0 1 2 2 0 2 0 -1 -1 -2 -1 1 -1 4 1
%e 1 -2 4 1 -2 0 -1 3 3 1 1 4 5 1 0 4
%e 0 4 -1 2 4 0 -1 -2 0 1 3 1 0 6 -1 2
%e 2 2 2 1 1 2 2 2 1 3 3 2 1 0 2 -2
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 04 2012
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