A216820 Number of polyominoes of site-perimeter n with 8-holes allowed.

1, 0, 2, 4, 12, 32, 110, 340, 1209, 4272, 16166, 61848, 246660, 1004883, 4209124, 18020832, 78898047, 352437205, 1605225878, 7445515638, 35142033027, 168644213617, 822311934788, 4071431204506, 20457850555113

Offset

4,3

Comments

This sequence counts fixed 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; A216819 allows holes but requires them to be connected to each other and to the exterior area via common corners; A216818 doesn't allow holes. - Andrey Zabolotskiy, Feb 02 2022

Links

Table of n, a(n) for n=4..28.

A. R. Conway and A. J. Guttmann, On two-dimensional percolation, J. Phys. A: Math. Gen., 28 (1995), 891-904. See Table 2.

J. Fortier, A. Goupil, J. Lortie and J. Tremblay, Exhaustive generation of gominoes, Theoretical Computer Science, 502 (2013), 76-87. See Table 1, beware of the typo in a(15).

Example

The only polyomino with site-perimeter 4 is a single cell.
No polyominoes have site-perimeter 5.
a(6) = 2: the domino, rotated (or reflected) in 2 possible ways.
a(7) = 4: the L-tromino, rotated in 4 ways.
a(8) = 12: the X-pentomino; the square tetromino; the straight tromino, rotated in 2 ways; the T-tetromino, rotated in 4 ways; the skew tetromino, rotated and reflected in 4 ways.

Crossrefs

Cf. A216818 (no holes), A216819 (holes connected by corners); A001168 (by area), A057730 (by perimeter); A366443 (free).

Sequence in context: A002528 A216818 A216819 * A148194 A289501 A274961

Adjacent sequences: A216817 A216818 A216819 * A216821 A216822 A216823

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 20 2012

Extensions

a(15) corrected, a(16)-a(28) from Conway & Guttmann added by Andrey Zabolotskiy, Feb 02 2022

Status

approved