A368863 Square array read by antidiagonals; the n-th row is the decimal expansion of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in diffusion-limited aggregation on the square lattice.

1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 0, 0, 4, 2, 0, 0, 0, 3, 1, 0, 0, 0, 0, 1, 3, 5, 0, 0, 0, 0, 7, 6, 3, 5, 0, 0, 0, 0, 1, 5, 3, 4, 5, 0, 0, 0, 0, 8, 6, 1, 6, 1, 3, 0, 0, 0, 0, 7, 2, 1, 2, 0, 7, 8, 0, 0, 0, 0, 2, 5, 7, 9, 7, 9, 1, 1, 0, 0, 0, 0, 2, 5, 4, 4, 5, 4, 3, 6, 1, 0, 0

Offset

1,5

Comments

The n-th row is the decimal expansion of the number on the n-th row of A368660 divided by A335573(n+1). See A368660 for details.

Rows A130866(k-1)+1 to A130866(k) correspond to k-celled polyominoes, k >= 2.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..1596 (first 56 antidiagonals).

Index entries for sequences related to polyominoes.

Example

Array begins:
  1.00000000000000000000... (monomino)
  0.50000000000000000000... (domino)
  0.14317187227209462175... (L tromino)
  0.21365625545581075649... (I tromino)
  0.05331174468766310877... (L tetromino)
  0.05462942885357382723... (square tetromino)
  0.05107523273680265528... (T tetromino)
  0.03794485956843370668... (S tetromino)
  0.08139812221208792734... (I tetromino)
  0.01652391644265825925... (P pentomino)
  0.01709341200261444870... (V pentomino)
  0.00933365290110550590... (W pentomino)
  0.01825698429438352158... (L pentomino)
  0.01973313069852314774... (Y pentomino)
  0.01316184592639931744... (N pentomino)
  0.01069856796007681265... (U pentomino)
  0.02067501830899727807... (T pentomino)
  0.01358243200363682514... (F pentomino)
  0.01232428737930631004... (Z pentomino)
  0.01279646275569121440... (X pentomino)
  0.02831865405554939733... (I pentomino)
  ...

Crossrefs

Cf. A000105, A001168, A130866, A246521, A335573, A368660 (free polyominoes), A368864, A368865.

Corresponding sequences for internal diffusion-limited aggregation: A368392, A368393.

Sequence in context: A196344 A106222 A368864 * A090750 A324656 A325817

Adjacent sequences: A368860 A368861 A368862 * A368864 A368865 A368866

Keyword

nonn,tabl,cons

Author

Pontus von Brömssen, Jan 08 2024

Status

approved