A366443 - OEIS

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A366443

Number of free polyominoes of site-perimeter n.

0, 0, 0, 1, 0, 1, 1, 5, 5, 23, 46, 187, 552, 2145, 7796

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OFFSET

1,8

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.

LINKS

Table of n, a(n) for n=1..15.

John Mason, Examples

EXAMPLE

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".

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).

Sequence in context: A338936 A175713 A090936 * A262117 A145764 A165826

Adjacent sequences: A366440 A366441 A366442 * A366444 A366445 A366446

KEYWORD

nonn,hard,more

AUTHOR

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

STATUS

approved