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%I #9 Mar 19 2018 04:10:40
%S 21,514,4029,18646,62853,172610,409199,870122,1699831,3104474,5365417,
%T 8858142,14068115,21614144,32266607,46975088,66888951,93389664,
%U 128113109,172986976,230254897,302518564,392763779,504407780,641326401,807907094
%N Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.
%C Row 7 of A209344.
%H R. H. Hardin, <a href="/A209348/b209348.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) - 2*a(n-5) + 5*a(n-6) - 5*a(n-7) + 3*a(n-8) - 3*a(n-10) + 5*a(n-11) - 5*a(n-12) + 2*a(n-13) - a(n-14) + a(n-15) + 2*a(n-16) - 3*a(n-17) + a(n-18).
%e Some solutions for n=5:
%e -5 -4 -4 -5 -5 -4 -4 -3 -2 -2 -4 -4 -5 -5 -5 -4
%e -5 -3 0 -4 0 -2 -3 -1 -1 -1 -3 -2 -2 -4 -3 1
%e -1 5 -4 2 0 -2 1 -2 -1 -2 4 3 -1 0 5 -3
%e 5 5 1 2 5 0 1 2 1 -1 1 3 5 4 2 -2
%e -4 -3 2 1 -1 2 5 2 -1 3 5 -4 3 2 -2 1
%e 5 -1 3 -1 -4 1 2 0 3 3 -4 0 -2 1 0 2
%e 5 1 2 5 5 5 -2 2 1 0 1 4 2 2 3 5
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 06 2012
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