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%I #8 Dec 27 2023 12:28:05
%S 1,4,7,35,145,770,4029,22739,130282,766177,4566523,27587850,168340643,
%T 1036444786,6429150260,40144480583
%N Number of n-bead necklaces labeled with numbers -3..3 allowing reversal, with sum zero with no three beads in a row equal.
%C Column 3 of A209344.
%e Some solutions for n=8:
%e .-3...-3...-3...-3...-3...-3...-2...-3...-3...-3...-3...-3...-3...-3...-3...-3
%e ..1....0...-2...-2....0....1....0....0...-1...-2...-1...-2....0....0...-2...-2
%e .-2...-1....1....1....0....1....2...-1...-2....2....0....2...-1....0...-2....0
%e ..1....3....2....1...-3...-2...-1...-1....2....1....3....3...-2...-1....3....0
%e ..0....0....2....0....1...-2....0....1....2....3....1....2....1....2....2....2
%e .-2....3...-2...-3....0....2....1...-2....0...-3...-2...-3....2....0....1...-1
%e ..3...-3...-1....3....2....1...-2....3....0...-1....3....2....0....1....0....2
%e ..2....1....3....3....3....2....2....3....2....3...-1...-1....3....1....1....2
%Y Cf. A209344.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 06 2012