A342537 Number of free polyominoes with n cells having simply-connected interiors.

1, 1, 2, 5, 12, 35, 108, 368, 1283, 4639, 17003, 63222, 236819, 893515, 3387953, 12904855, 49335965, 189243115

Offset: 1

Author

John Mason, Allan C. Wechsler, Mar 15 2021

Keywords

• nonn
• more

Comments

The polyominoes referred to in the definition are those having a single traceable perimeter. The definition therefore includes the heptomino with a hole, as in this case the border, although not self-avoiding (it meets itself at a corner) is still traceable; it excludes the square octomino with a hole, whose border consists of two distinct polygons. Thus starting from n=8, A000104(n) < a(n) < A000105(n).

Crossrefs

Cf. A000104 (free polyominoes without holes), A000105 (free polyominoes).

Extensions

a(17)-a(18) from John Mason, Jan 04 2023