%I #11 Mar 18 2018 17:29:06
%S 57,1163,8671,39019,129823,353333,833253,1764925,3438877,6267735,
%T 10816499,17836183,28300819,43447825,64821737,94321305,134249953,
%U 187369603,256957863,346868579,461595751,606340813,787083277,1010654741
%N Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
%C Row 7 of A208597.
%H R. H. Hardin, <a href="/A208601/b208601.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (841/180)*n^6 + (841/60)*n^5 + (325/18)*n^4 + (51/4)*n^3 + (949/180)*n^2 + (37/30)*n + 1.
%F Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F G.f.: x*(57 + 764*x + 1727*x^2 + 750*x^3 + 71*x^4 - 6*x^5 + x^6) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=4:
%e -4 -2 -4 -4 -4 -3 -3 -4 -2 -4 -4 -3 -3 -3 -4 -4
%e -2 -2 3 1 -2 2 0 -4 2 -1 2 -1 0 1 2 2
%e 3 1 2 -2 0 0 -1 -2 1 2 -2 0 1 0 -3 -4
%e 1 2 1 0 3 2 2 1 1 -4 1 0 0 1 4 4
%e -2 -2 -1 2 3 -3 -1 1 -1 3 -3 -1 -2 -2 -4 1
%e 1 1 -1 -1 -3 3 2 4 0 3 2 2 2 1 3 -2
%e 3 2 0 4 3 -1 1 4 -1 1 4 3 2 2 2 3
%Y Cf. A208597.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 29 2012