A368000 a(n) is the numerator 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 as the image of a simple random walk on the square lattice.

1, 1, 1, 1, 1, 4, 1, 1, 1, 97, 1, 1, 1, 8, 1, 1, 8, 8, 1, 1, 1, 867, 9565, 1, 1, 2495, 1, 262781, 389, 9565, 389, 262781, 1, 867, 1, 597, 389, 1, 631381, 597, 389, 1, 1, 389, 1, 597, 1, 1, 389, 597, 389, 1, 597, 2501, 412, 1, 2635, 1706571966622, 1706571966622, 1117, 1117

Offset

1,6

Comments

In a simple random walk on the square lattice, draw a unit square around each visited point. a(n)/A368001(n) is the probability that, when the appropriate number of distinct points have been visited, the drawn squares form a particular one of the fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1).

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

Links

Table of n, a(n) for n=1..61.

Index entries for sequences related to polyominoes.

Formula

a(n)/A368001(n) = (A367994(n)/A367995(n))/A335573(n+1).

Example

As an irregular triangle:
   1;
   1;
   1, 1;
   1, 4, 1, 1, 1;
  97, 1, 1, 1, 8, 1, 1, 8, 8, 1, 1, 1;
  ...

Crossrefs

Cf. A000105, A246521, A335573, A367675, A367764, A367994, A367995, A368001 (denominators), A368002, A368004.

Sequence in context: A178649 A353976 A363919 * A335502 A119591 A333782

Adjacent sequences: A367997 A367998 A367999 * A368001 A368002 A368003

Keyword

nonn,frac,tabf

Author

Pontus von Brömssen, Dec 09 2023

Status

approved