A368865 Square array read by antidiagonals; the n-th row is the decimal expansion of the maximum 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, 2, 0, 0, 0, 1, 0, 0, 0, 0, 3, 8, 0, 0, 0, 0, 6, 1, 2, 0, 0, 0, 0, 5, 3, 8, 0, 0, 0, 0, 0, 6, 9, 3, 9, 0, 0, 0

Offset

1,5

Comments

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

It seems that the straight polyomino is the unique n-celled polyomino that has the maximum probability of appearing in a fixed orientation. If true, the n-th row here equals the A130866(n)-th row of A368863.

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)
  0.21365625545581075649... (4th row of A368863)
  0.08139812221208792734... (9th row of A368863)
  0.02831865405554939733... (21st row of A368863)
  0.00913650301189504691... (56th row of A368863)
  ...

Crossrefs

Cf. A130866, A368394 (internal diffusion-limited aggregation), A368662 (free polyominoes), A368863, A368864 (minimum).

Sequence in context: A325967 A229656 A216722 * A036297 A336530 A087935

Adjacent sequences: A368862 A368863 A368864 * A368866 A368867 A368868

Keyword

nonn,tabl,cons,more

Author

Pontus von Brömssen, Jan 08 2024

Status

approved