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

1,11

Comments

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

Links

Table of n, a(n) for n=1..20.

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

Example

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

Crossrefs

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

Cf. A245660 (unitary polyominoes without holes).

Sequence in context: A361440 A143590 A336030 * A059348 A110871 A243856

Adjacent sequences: A245617 A245618 A245619 * A245621 A245622 A245623

Keyword

nonn,hard,more,nice

Author

George Sicherman, Jul 27 2014

Status

approved