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A342536
Number of self-avoiding polygons on the square lattice, of perimeter 2n, with the property that all the right-angles of the same orientation are contiguous.
1
1, 1, 3, 4, 10, 17, 36, 65, 126, 227, 419, 743, 1323, 2295, 3965
OFFSET
2,3
COMMENTS
For any polygon, build a bracelet of black and white beads by following the border of the polygon in a clockwise direction, adding a black bead for each right-turning right angle, and a white bead for each left-turning right angle. The polygons counted by this sequence are those whose bracelets have all the black beads together and all the white beads together.
EXAMPLE
a(4)=3, as there are 3 self-avoiding polygons (SAPs) of perimeter 8 that satisfy the condition; these are the polygons corresponding to the strip and L-shaped trominoes, and the square tetromino.
CROSSREFS
Cf. A266549.
Sequence in context: A051437 A224073 A034774 * A172416 A317883 A337089
KEYWORD
nonn,more
AUTHOR
STATUS
approved