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

1,5

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.

Links

Table of n, a(n) for n=1..45.

Index entries for sequences related to polyominoes.

Example

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):
                                _        _ _
       _      _      _ _      _| |     _|  _|
  _   | |   _| |   _|  _|   _|  _|   _|  _|
 |_|  |_|  |_ _|  |_ _|    |_ _|    |_ _|

Crossrefs

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

Sequence in context: A101194 A196344 A106222 * A368863 A090750 A324656

Adjacent sequences: A368861 A368862 A368863 * A368865 A368866 A368867

Keyword

nonn,tabl,cons,more

Author

Pontus von Brömssen, Jan 08 2024

Status

approved