A368004 Numerator of the greatest probability that a particular fixed polyomino with n cells appears as the image of a simple random walk on the square lattice.

1, 1, 1, 4, 97, 2495, 98576101, 790070277194753299070819, 1697817285476742288131092, 301424494727669492958807965129775458632594691220000993251280413656197020195992465248816242330162

Offset: 1

Author

Pontus von Brömssen, Dec 21 2023

Keywords

• nonn
• frac

Comments

a(n) is the numerator of the maximum of A368000/A368001 over the n-th row. See A368000 for details.

Examples

			For 1 <= n <= 13, the following are all polyominoes, up to reflections and rotations, that have the maximum probabilities for their respective sizes. Except for n = 3, there is just one such polyomino (again, up to reflections and rotations).
                    _           _
        _    _     | |   _ _   | |_
   _   | |  | |_   | |  |   |  |   |
  |_|  |_|  |_ _|  |_|  |_ _|  |_ _|
   _ _      _ _    _ _      _ _ _
  |   |   _|   |  |   |_   |     |
  |   |  |    _|  |     |  |     |
  |_ _|  |_ _|    |_ _ _|  |_ _ _|
     _ _    _ _      _ _ _      _ _
   _|   |  |   |_   |     |   _|   |_
  |     |  |     |  |     |  |       |
  |    _|  |     |  |     |  |      _|
  |_ _|    |_ _ _|  |_ _ _|  |_ _ _|
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..13
• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A367677, A367766, A367998, A368000, A368001, A368002, A368005 (denominators).