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, 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.

Links

Table of n, a(n) for n=2..16.

John Mason, Contiguously oriented saps

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

Adjacent sequences: A342533 A342534 A342535 * A342537 A342538 A342539

Keyword

nonn,more

Author

John Mason, Allan C. Wechsler, Mar 15 2021

Status

approved