A216820 -id:A216820 - cp's OEIS frontend

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

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

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.

			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".

John Mason, Examples

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).

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

A216819 Number of simply 8-connected polyominoes of site-perimeter n.

Original entry on oeis.org

1, 0, 2, 4, 12, 32, 110, 340, 1209, 4256, 15974, 60232

Offset: 4

N. J. A. Sloane, Sep 20 2012

J. Fortier, A. Goupil, J. Lortie and J. Tremblay, Exhaustive generation of gominoes, Theoretical Computer Science, 502 (2013), 76-87.

Cf. A216818 (no holes), A216820 (any holes).

A342537 counts free (rather than fixed) polyominoes with given area (rather than site-perimeter).

cp's OEIS Frontend

A366443 Number of free polyominoes of site-perimeter n.

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