A245660 -id:A245660 - cp's OEIS frontend

A245620 Number of unitary polyominoes with n cells. A unitary polyomino is a polyomino whose edges all have length 1.

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 3, 4, 7, 10, 17, 28, 47, 69

Offset: 1

George Sicherman, Jul 27 2014

If a unitary polyomino is colored in checks, all cells on each boundary have the same color. This characterizes unitary polyominoes.

			The monomino (a single square) is unitary.  The domino, trominoes, and tetrominoes are not.  The X pentomino is unitary; the other pentominoes are not.

Alberto Del Lungo, Massimo Mirolli, Renzo Pinzani, and Simone Rinaldi, A Bijection for Directed Polyominoes, Discrete Mathematics and Theoretical Computer Science Proceedings, AA (2001), 133-144.
George Sicherman, Catalogue of Unitary Polyominoes

Cf. A000105 (number of free polyominoes with n cells).

Cf. A245660 (unitary polyominoes without holes).

A362708 a(n) is the number of almost unitary polyominoes of size n. An almost unitary polyomino is one in which all but 1 of its perimeter walls have length 1.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 2, 2, 1, 6, 9, 11, 21, 49, 69, 117, 249, 427

Offset: 1

John Mason, Apr 30 2023

			a(4)=1 because of:
  O
  OO
  O

George Sicherman, Catalogue of Almost Unitary Polyominoes

Cf. A245660, A362709.

A362709 a(n) is the number of almost almost unitary polyominoes of size n. An almost almost unitary polyomino is one in which all but 2 of its perimeter walls have length 1.

Original entry on oeis.org

0, 1, 2, 2, 4, 12, 15, 29, 58, 116, 199, 403, 790, 1509, 2857, 5700, 10941, 21032

Offset: 1

John Mason, Apr 30 2023

			a(4)=2 because of:
  O  O
  O  OO
  O   O
  O

George Sicherman, Catalogue of Almost Almost Unitary Polyominoes

Cf. A245660, A362708.

cp's OEIS Frontend

A245620 Number of unitary polyominoes with n cells. A unitary polyomino is a polyomino whose edges all have length 1.

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A362708 a(n) is the number of almost unitary polyominoes of size n. An almost unitary polyomino is one in which all but 1 of its perimeter walls have length 1.

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A362709 a(n) is the number of almost almost unitary polyominoes of size n. An almost almost unitary polyomino is one in which all but 2 of its perimeter walls have length 1.

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Author

Keywords

Examples

Links

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