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%I #8 Mar 18 2018 17:29:28
%S 6,86,576,2517,8235,22249,52208,110285,214440,390344,672932,1108883,
%T 1758433,2698447,4024458,5854361,8330650,11624758,15939472,21513945,
%U 28626249,37599103,48802532,62660333,79652814,100324030,125284570
%N Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.
%C Row 7 of A209032.
%H R. H. Hardin, <a href="/A209035/b209035.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical: a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-8) + a(n-10) + a(n-11) + 2*a(n-12) - 2*a(n-16) - a(n-17) - a(n-18) + a(n-20) + a(n-21) + a(n-23) - a(n-26) - a(n-27) + a(n-28).
%e Some solutions for n=6:
%e -5 -4 -5 -4 -2 -4 -3 -3 -5 -4 -3 -3 -3 -2 -6 -3
%e -2 -3 -4 -1 0 1 -1 -2 0 -2 2 1 2 -1 -5 -2
%e 0 3 -1 0 1 -1 1 1 -2 -3 -1 1 -2 1 -1 3
%e 1 3 2 5 -2 2 1 2 3 0 -1 -2 3 -2 1 1
%e 4 0 4 1 1 1 2 1 0 5 -2 -2 -1 -1 5 -1
%e 4 2 3 -2 1 -1 1 3 3 4 3 3 -2 5 6 0
%e -2 -1 1 1 1 2 -1 -2 1 0 2 2 3 0 0 2
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 04 2012
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