A380286 Number of distinct values of the number of regions between the free polyominoes with n cells and their bounding boxes.

1, 1, 2, 3, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10

Offset

1,3

Comments

The regions include any holes in the polyominoes.

Links

Table of n, a(n) for n=1..16.

Index entries for sequences related to polyominoes.

Example

Illustration for n = 4:
The free polyominoes with four cells are also called free tetrominoes.
The five free tetrominoes are as shown below:
    _
   |_|     _       _       _
   |_|    |_|     |_|_    |_|_     _ _
   |_|    |_|_    |_|_|   |_|_|   |_|_|
   |_|    |_|_|     |_|   |_|     |_|_|
.
The bounding boxes are respectively as shown below:
    _
   | |     _ _     _ _     _ _
   | |    |   |   |   |   |   |    _ _
   | |    |   |   |   |   |   |   |   |
   |_|    |_ _|   |_ _|   |_ _|   |_ _|
.
From left to right the number of regions between the free tetrominoes and their bounding boxes are respectively [0, 1, 2, 2, 0], hence there are three distinct values of the number of regions, they are [0, 1, 2], so a(4) = 3.
.

Crossrefs

Row lengths of A380282.

Cf. A000105, A379627, A379628, A380283, A380284, A380285.

Sequence in context: A102642 A183228 A133304 * A246401 A003660 A065688

Adjacent sequences: A380283 A380284 A380285 * A380287 A380288 A380289

Keyword

nonn,more,new

Author

Omar E. Pol, Jan 24 2025

Extensions

a(8)-a(16) from Pontus von Brömssen, Jan 24 2025

Status

approved