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Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.
1

%I #9 Mar 18 2018 17:54:34

%S 3,23,157,703,2313,6261,14701,31069,60429,109991,189627,312461,495497,

%T 760323,1133925,1649437,2347063,3275011,4490479,6060743,8064195,

%U 10591639,13747397,17650689,22436937,28259205,35289631,43720971,53768203,65670121

%N Number of 7-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.

%C Row 7 of A209007.

%H R. H. Hardin, <a href="/A209011/b209011.txt">Table of n, a(n) for n = 1..79</a>

%e Some solutions for n=6:

%e -3 -1 -3 -4 -5 -4 -5 -5 -4 -5 -4 -4 -3 -2 -3 -6

%e -1 -1 0 -3 -2 -2 -5 -5 -1 -1 -3 -2 -2 -1 -1 -1

%e 2 -1 1 -2 3 -2 0 1 0 2 -2 0 -1 1 -2 4

%e 0 -1 4 3 2 3 4 4 4 0 2 1 1 3 1 4

%e 2 3 1 4 4 3 4 4 2 4 2 2 3 0 3 4

%e 1 1 -1 4 1 2 3 1 1 3 4 3 2 0 2 0

%e -1 0 -2 -2 -3 0 -1 0 -2 -3 1 0 0 -1 0 -5

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2012