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

1,3

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).

Links

Table of n, a(n) for n=1..18.

Crossrefs

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

Sequence in context: A148287 A036357 A000104 * A000105 A055192 A108555

Adjacent sequences: A342534 A342535 A342536 * A342538 A342539 A342540

Keyword

nonn,more

Author

John Mason, Allan C. Wechsler, Mar 15 2021

Extensions

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

Status

approved