Pontus von Brömssen, <a href="/A367998/b367998_1.txt">Table of n, a(n) for n = 1..13</a>.

proposed

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editing

proposed

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

Pontus von Brömssen, <a href="/A367998/b367998_1.txt">Table of n, a(n) for n = 1..13</a>.

allocated for Pontus von BrömssenNumerator 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

1,3

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

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

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.

_ _ _ _

_ _ | | | |_ | |

_ | | | |_ | |_ | | | |

|_| |_| |_ _| |_ _| |_ _| |_ _|

_ _ _

_ _ | |_ _ _ _| |

| | | | | |_ | _|

| |_ | | | | | |

|_ _ _| |_ _| |_ _ _| |_ _|

_ _ _ _ _ _ _ _ _

| | | |_ _| |_ _| |

| |_ | | | | | _|

| | | | | _ _| | |

|_ _ _| |_ _ _| |_ _| |_ _ _|

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

allocated

nonn,frac

Pontus von Brömssen, Dec 08 2023

approved

editing

allocated for Pontus von Brömssen

allocated

approved