A368004 - OEIS

%I #5 Dec 21 2023 15:44:30

%S 1,1,1,4,97,2495,98576101,790070277194753299070819,

%T 1697817285476742288131092,

%U 301424494727669492958807965129775458632594691220000993251280413656197020195992465248816242330162

%N 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.

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

%H Pontus von Brömssen, <a href="/A368004/b368004.txt">Table of n, a(n) for n = 1..13</a>

%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.

%e 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).

%e                     _           _

%e         _    _     | |   _ _   | |_

%e    _   | |  | |_   | |  |   |  |   |

%e   |_|  |_|  |_ _|  |_|  |_ _|  |_ _|

%e    _ _      _ _    _ _      _ _ _

%e   |   |   _|   |  |   |_   |     |

%e   |   |  |    _|  |     |  |     |

%e   |_ _|  |_ _|    |_ _ _|  |_ _ _|

%e      _ _    _ _      _ _ _      _ _

%e    _|   |  |   |_   |     |   _|   |_

%e   |     |  |     |  |     |  |       |

%e   |    _|  |     |  |     |  |      _|

%e   |_ _|    |_ _ _|  |_ _ _|  |_ _ _|

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

%K nonn,frac

%O 1,4

%A _Pontus von Brömssen_, Dec 21 2023