cp's OEIS Frontend

A368000 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.

%I A368000 #5 Dec 21 2023 15:41:48
%S A368000 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 A368000 262781,389,9565,389,262781,1,867,1,597,389,1,631381,597,389,1,1,389,
%U A368000 1,597,1,1,389,597,389,1,597,2501,412,1,2635,1706571966622,1706571966622,1117,1117
%N A368000 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 A368000 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 A368000 Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.
%H A368000 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%F A368000 a(n)/A368001(n) = (A367994(n)/A367995(n))/A335573(n+1).
%e A368000 As an irregular triangle:
%e A368000    1;
%e A368000    1;
%e A368000    1, 1;
%e A368000    1, 4, 1, 1, 1;
%e A368000   97, 1, 1, 1, 8, 1, 1, 8, 8, 1, 1, 1;
%e A368000   ...
%Y A368000 Cf. A000105, A246521, A335573, A367675, A367764, A367994, A367995, A368001 (denominators), A368002, A368004.
%K A368000 nonn,frac,tabf
%O A368000 1,6
%A A368000 _Pontus von Brömssen_, Dec 09 2023