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%I #9 Mar 18 2018 17:53:13
%S 2,10,46,153,409,923,1854,3477,6034,9876,15590,23625,34577,49487,
%T 69002,94129,126458,166848,216732,278575,353347,442987,550942,678467,
%U 827960,1004068,1208150,1443457,1715865,2026795,2380232,2783955,3239122,3750544
%N Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.
%C Row 6 of A209007.
%H R. H. Hardin, <a href="/A209010/b209010.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) - a(n-2) + 3*a(n-3) - 2*a(n-4) + 2*a(n-5) - 3*a(n-6) + a(n-7) - a(n-8) + a(n-9) + a(n-10) - a(n-11) + 3*a(n-12) - 5*a(n-13) + 4*a(n-14) - 8*a(n-15) + 7*a(n-16) - 5*a(n-17) + 7*a(n-18) - 3*a(n-19) + 2*a(n-20) - 2*a(n-21) - 2*a(n-22) + 2*a(n-23) - 3*a(n-24) + 7*a(n-25) - 5*a(n-26) + 7*a(n-27) - 8*a(n-28) + 4*a(n-29) - 5*a(n-30) + 3*a(n-31) - a(n-32) + a(n-33) + a(n-34) - a(n-35) + a(n-36) - 3*a(n-37) + 2*a(n-38) - 2*a(n-39) + 3*a(n-40) - a(n-41) + a(n-42) - a(n-43).
%e Some solutions for n=6:
%e -2 -2 -2 -2 -3 -4 -2 -2 -3 -2 -4 -4 -1 -1 -2 -5
%e -1 0 0 -2 -3 -3 -1 -1 -1 -1 -3 -4 1 0 0 -1
%e 3 0 -2 2 2 0 0 1 -1 2 3 2 0 0 -1 2
%e 1 -2 0 2 4 4 -1 0 3 0 5 4 -1 -1 1 4
%e 0 2 3 1 2 3 3 1 1 2 1 1 1 2 3 3
%e -1 2 1 -1 -2 0 1 1 1 -1 -2 1 0 0 -1 -3
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 04 2012
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