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Number of n-bead necklaces labeled with numbers -4..4 not allowing reversal, with sum zero and first and second differences in -4..4.
0

%I #6 Mar 13 2017 00:09:53

%S 1,2,3,10,31,153,703,3393,16001,75381,357369,1713043,8299559,40613618,

%T 200412275,995895544

%N Number of n-bead necklaces labeled with numbers -4..4 not allowing reversal, with sum zero and first and second differences in -4..4.

%C Column 4 of A209007.

%e Some solutions for n=6:

%e .-1...-3...-2...-2...-2...-1...-3...-3...-1...-2...-2...-2...-3...-2...-2....0

%e ..0...-3....1....0...-2....1...-1...-3....0....1...-1....0...-1...-2....0....0

%e ..1....1....1....0....0...-1....2....1....0....2....1....0....2....0...-1....0

%e .-1....1....0....2....3....1....3....2....1....0....2....1....2....2....2....0

%e ..0....3....1....1....2....0....0....3...-1....0....1....1....2....2....1....0

%e ..1....1...-1...-1...-1....0...-1....0....1...-1...-1....0...-2....0....0....0

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 04 2012