%I #5 Dec 21 2023 15:41:48

%S 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,

%T 262781,389,9565,389,262781,1,867,1,597,389,1,631381,597,389,1,1,389,

%U 1,597,1,1,389,597,389,1,597,2501,412,1,2635,1706571966622,1706571966622,1117,1117

%N 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.

%C 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).

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

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

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

%e As an irregular triangle:

%e 1;

%e 1;

%e 1, 1;

%e 1, 4, 1, 1, 1;

%e 97, 1, 1, 1, 8, 1, 1, 8, 8, 1, 1, 1;

%e ...

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

%K nonn,frac,tabf

%O 1,6

%A _Pontus von Brömssen_, Dec 09 2023