%I #8 Mar 18 2018 18:36:06
%S 5,51,253,874,2354,5404,11010,20553,35781,58971,92851,140818,206798,
%T 295528,412352,563577,756175,998245,1298615,1667392,2115476,2655216,
%U 3299792,4064019,4963585,6015983,7239629,8654930,10283232,12148080
%N Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.
%C Row 6 of A208993.
%H R. H. Hardin, <a href="/A208997/b208997.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 -3 -4 -5 -3 -2 -3 -4 -4 -4 -4 -4 -3 -5 -4 -2 -2
%e 0 1 1 -3 -2 2 1 -1 1 0 2 1 1 2 -1 -2
%e 4 -2 6 1 1 -2 -2 4 1 5 3 -2 -1 0 1 2
%e 1 0 0 3 0 -1 4 2 2 3 -1 3 5 -2 -1 1
%e 0 3 -2 4 2 1 1 -2 1 -2 1 -1 2 3 4 1
%e -2 2 0 -2 1 3 0 1 -1 -2 -1 2 -2 1 -1 0
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 04 2012
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