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Number of n-bead necklaces labeled with numbers -1..1 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 23:33:22

%S 1,2,1,4,4,11,15,43,77,199,423,1080,2514,6355,15529,39429,98875,

%T 252551,643133,1653677,4254070,11005241,28518931,74179434,193328017,

%U 505236093,1322919905,3471492272,9125743338

%N Number of n-bead necklaces labeled with numbers -1..1 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

%C Column 1 of A209485.

%e Some solutions for n=10:

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

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

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

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

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

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 09 2012