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

Author

N. J. A. Sloane, Sep 20 2012

Keywords

• nonn
• more

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

Examples

			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.
		

Links

• 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).

Crossrefs

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

Extensions

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