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Number of n-bead necklaces labeled with numbers -3..3 not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
0

%I #6 Mar 12 2017 23:55:20

%S 1,4,11,55,261,1373,7377,41256,235639,1372782,8114465,48564722,

%T 293656843,1791382922,11011083783,68131049950,424018776003

%N Number of n-bead necklaces labeled with numbers -3..3 not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

%C Column 3 of A209115.

%e Some solutions for n=6:

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

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 05 2012