A368864 Square array read by antidiagonals; the n-th row is the decimal expansion of the minimum probability that a particular fixed polyomino with n cells appears in diffusion-limited aggregation on the square lattice.

1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 1, 7, 0, 0, 0, 0, 0, 7, 9, 9, 0, 0, 0, 0, 0, 1, 4, 3, 2, 0, 0, 0

Offset: 1

Author

Pontus von Brömssen, Jan 08 2024

Keywords

• nonn
• tabl
• cons
• more

Comments

The n-th row is the decimal expansion of the minimum of the numbers corresponding to rows A130866(n-1)+1..A130866(n) of A368863.

It seems that the zig-zag polyomino is the unique n-celled polyomino that has the minimum probability of appearing in a fixed orientation.

Examples

			Array begins:
  1.00000000000000000000... (1st row of A368863)
  0.50000000000000000000... (2nd row of A368863)
  0.14317187227209462175... (3rd row of A368863)
  0.03794485956843370668... (8th row of A368863)
  0.00933365290110550590... (12th row of A368863)
  0.00216801081906196078... (42nd row of A368863)
  ...
The corresponding polyominoes for 1 <= n <= 6 are (all these are unique):
                                _        _ _
       _      _      _ _      _| |     _|  _|
  _   | |   _| |   _|  _|   _|  _|   _|  _|
 |_|  |_|  |_ _|  |_ _|    |_ _|    |_ _|
		

Links

• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A130866, A368661 (free polyominoes), A368863, A368865 (maximum).