A367998 Numerator of the greatest probability that a particular free polyomino with n cells appears as the image of a simple random walk on the square lattice.

1, 1, 2, 8, 388, 2495, 13652575732976, 1580140554389506598141638, 2303282945504494379369753334706333784257298061180917309, 1116351824215919296474220471583292515147278170740521646743561595082143234790184233409933250330039986837258312677349601942095851

Offset: 1

Author

Pontus von Brömssen, Dec 08 2023

Keywords

• nonn
• frac

Comments

a(n) is the numerator of the maximum of A367994/A367995 over the n-th row. See A367994 for details.

Examples

			For 1 <= n <= 13, the following are all polyominoes that have the maximum probabilities for their respective sizes. Except for n = 7, there is just one such polyomino.
                    _      _      _ _
        _    _     | |    | |_   |   |
   _   | |  | |_   | |_   |   |  |   |
  |_|  |_|  |_ _|  |_ _|  |_ _|  |_ _|
            _                 _ _
   _ _     | |_    _ _      _|   |
  |   |    |   |  |   |_   |    _|
  |   |_   |   |  |     |  |   |
  |_ _ _|  |_ _|  |_ _ _|  |_ _|
   _ _      _ _        _ _        _ _ _
  |   |    |   |_    _|   |_    _|     |
  |   |_   |     |  |       |  |      _|
  |     |  |     |  |    _ _|  |     |
  |_ _ _|  |_ _ _|  |_ _|      |_ _ _|
		

Links

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

Crossrefs

Cf. A367673, A367762, A367994, A367995, A367996, A367999 (denominators), A368004.