A365621 Minimum size of a set of polyominoes with n cells such that all other free polyominoes with n cells can be obtained by moving one cell of one of the polyominoes in the set.

1, 1, 1, 1, 2, 3, 7

Offset: 1

Author

Pontus von Brömssen, Nov 14 2023

Keywords

• nonn
• more

Comments

a(n) is the domination number of the n-omino graph defined in A098891.

The intermediate (the set of cells remaining when the cell to be moved is detached) does not have to be a connected (n-1)-omino.

a(8) <= 18, a(9) <= 53.

Apparently, a(n) is close to A367441(n-1) for 3 <= n <= 9. Is this just a coincidence?

Examples

			For n <= 3, any one polyomino with n cells is enough to construct the others (if any) by moving one cell, so a(n) = 1.
For n = 4, either the L or the T tetromino suffices to construct the other four, so a(4) = 1.
Below are examples of sets of a(n) polyominoes that are sufficient to construct all other polyominoes with n cells, 5 <= n <= 7:
   _
  | |     _
  | |_   | |_
  |  _|  |   |
  |_|    |_ _|
   _
  | |     _
  | |    | |       _ _
  | |    | |_    _|  _|
  | |_   |   |  |   |
  |_ _|  |_ _|  |_ _|
   _
  | |                                  _
  | |     _        _          _       | |           _        _
  | |    | |_     | |_       | |      | |_      _ _| |      | |
  | |_   |  _|    |_  |     _| |_    _|  _|   _|  _ _|   _ _| |_
  |  _|  | |_ _    _| |_   |    _|  |  _|    |  _|      |  _ _ _|
  |_|    |_ _ _|  |_ _ _|  |_ _|    |_|      |_|        |_|
		

Links

• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A098891, A367123, A367124, A367127, A367441.