A209478 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.

1, 2, 1, 4, 4, 11, 15, 43, 77, 199, 423, 1080, 2514, 6355, 15529, 39429, 98875, 252551, 643133, 1653677, 4254070, 11005241, 28518931, 74179434, 193328017, 505236093, 1322919905, 3471492272, 9125743338

Offset

1,2

Comments

Column 1 of A209485.

Links

Table of n, a(n) for n=1..29.

Example

Some solutions for n=10:
.-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1
.-1....0...-1...-1...-1....0...-1...-1....0....0....0....0...-1...-1...-1...-1
..1....0....0....0....1....0....1....1...-1...-1...-1....0...-1....0....0....0
.-1...-1....0....0...-1...-1...-1...-1....1....1....1....1....1....0....0....0
..0....0....0....1....1....0....0....0...-1...-1....0...-1...-1....1....0....0
..0....0....0....1...-1....0....0....0....0....1....0....0....1....0....0....0
..0....0....0...-1....1....1...-1....0....0...-1...-1....0....1....0....1....1
..0....0....1...-1...-1....0....1....1....1....1....1....1....0...-1...-1....1
..1....1....0....1....1....0....1....0....0....0....0....0....0....1....1....0
..1....1....1....1....1....1....1....1....1....1....1....0....1....1....1....0

Crossrefs

Sequence in context: A241513 A095293 A034409 * A211178 A048049 A212716

Adjacent sequences: A209475 A209476 A209477 * A209479 A209480 A209481

Keyword

nonn

Author

R. H. Hardin, Mar 09 2012

Status

approved