A366443 Number of free polyominoes of site-perimeter n.

0, 0, 0, 1, 0, 1, 1, 5, 5, 23, 46, 187, 552, 2145, 7818

Offset: 1

Author

John Mason from an idea of Allan C. Wechsler, Oct 10 2023

Keywords

• nonn
• hard
• more

Comments

This sequence counts free connected (via common edges) polyominoes with given site-perimeter. The site-perimeter of a polyomino is the number of cells that are adjacent to it (via common edges). This sequence allows holes of any kind.

Examples

			a(4) = a(6) = a(7) = 1 as the monomino, domino and L-shaped tromino are the only polyominoes with site perimeter 4, 6 and 7 respectively.
a(5) = 0 as no polyomino has a site-perimeter of 5.
a(8) = 5 as the straight tromino, square tetromino, T-tetromino, S-tetromino and cross pentomino are the only polyominoes with site perimeter 8. See link "Examples".
		

Links

• John Mason, Examples

Crossrefs

Cf. A000105 (free polyominoes), A001971 (the maximum size of a polyomino with site-perimeter n is given by A001971(n-2)), A057730 (perimeter instead of site-perimeter), A216820 (fixed version of current sequence).

Column sums of A338211 (without the column for 0-celled polyominoes).

Extensions

a(15) corrected by Sean A. Irvine, Apr 13 2025