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

%I #7 Mar 13 2017 00:18:00

%S 1,1,1,2,3,5,9,18,35,73,151,324,691,1503,3277,7212,15927,35407,78967,

%T 176942,397717,897079,2029071,4602438,10464647,23849545,54468627,

%U 124646180,285762575,656268311,1509570433,3477615648,8022765075

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

%C Column 1 of A208993.

%H R. H. Hardin, <a href="/A208986/b208986.txt">Table of n, a(n) for n = 1..35</a>

%e All solutions for n=7:

%e ..0...-1...-1...-1...-1...-1...-1...-1...-1

%e ..0...-1...-1...-1....0....0....0....0....0

%e ..0....0....0....0....0....0....0....1...-1

%e ..0....1....1....0....0....0....1....0....0

%e ..0....1....0....1....1....0....0....0....1

%e ..0....0....1....1....0....1....0....0....1

%e ..0....0....0....0....0....0....0....0....0

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 04 2012