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%I #6 Mar 12 2017 23:50:47
%S 1,2,1,4,5,14,21,51,102,249,555,1358,3201,7890,19232,47869,118955,
%T 298875,752039,1904621,4835666,12330144,31521037,80836979,207803455,
%U 535535393,1383064966,3579351724,9280561947
%N Number of n-bead necklaces labeled with numbers -1..1 allowing reversal, with sum zero with no three beads in a row equal.
%C Column 1 of A209344.
%e Some solutions for n=10:
%e .-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1
%e ..0....0...-1....0...-1....0....0....0....0...-1....0....0....0....0....0....0
%e .-1....0....0....0....0....0....0...-1...-1....0...-1....0....0...-1....1...-1
%e ..0...-1....0....1...-1...-1...-1....0....0...-1....1...-1....1....1....0....0
%e ..0....0...-1....0....1....0....1....1....1....1....1....0...-1...-1...-1....0
%e ..1....1....0...-1....0....0...-1...-1...-1....1...-1....1....1....1....1....1
%e ..1....0....1....1....1....1....1....1....1...-1....0...-1....0....0...-1....0
%e ..0....1....0...-1....0....0....0....0...-1....1...-1....0....0....1....1....1
%e .-1...-1....1....1....1....0....0....0....1....0....1....1...-1...-1...-1....0
%e ..1....1....1....0....0....1....1....1....1....1....1....1....1....1....1....0
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 06 2012