A367441 Minimum size of a set of polyominoes with n-1 cells such that all free polyominoes with n cells can be obtained by adding one cell to one of the polyominoes in the set.

1, 1, 2, 4, 8, 19

Offset

2,3

Comments

a(8) <= 54, a(9) <= 160.

Apparently, a(n) is close to A365621(n+1) for n <= 8. Is this just a coincidence?

Links

Table of n, a(n) for n=2..7.

Index entries for sequences related to polyominoes.

Example

For n <= 4, all polyominoes with n-1 cells are needed to obtain all polyominoes with n cells by adding one cell, so a(n) = A000105(n-1).
For n = 5, all but the square tetromino are needed to obtain all pentominoes, so a(5) = A000105(4)-1 = 4.
For n = 6, there are 5 different sets of a(6) = 8 pentominoes that are sufficient to obtain all hexominoes. One of these sets consists of the I, L, N, P, U, V, W, and Y pentominoes. The X pentomino is the only pentomino that does not appear in any of these sets. The I, L, N, and W pentominoes are needed in all such sets.
For n = 7, there are 8 different sets of a(7) = 19 hexominoes that are sufficient to obtain all heptominoes. 14
hexominoes appear in all these sets, 10 appear in none of them.

Crossrefs

Cf. A000105, A365621, A367435, A367440, A367443.

Sequence in context: A180206 A058374 A007881 * A293542 A049960 A018306

Adjacent sequences: A367438 A367439 A367440 * A367442 A367443 A367444

Keyword

nonn,more

Author

Pontus von Brömssen, Nov 18 2023

Status

approved