cp's OEIS Frontend

A368001 a(n) is the denominator 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 A368001 #5 Dec 21 2023 15:41:58
%S A368001 1,2,6,6,21,21,28,21,21,2002,77,77,77,1001,77,77,1001,1001,77,91,77,
%T A368001 89089,785603,286,286,48594,286,25924899,194194,785603,194194,
%U A368001 25924899,286,89089,286,388388,194194,286,51849798,388388,194194,286,286,194194,286,388388,286,286,194194,388388,194194,286,388388,1165164,291291,286
%N A368001 a(n) is the denominator 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 A368001 In a simple random walk on the square lattice, draw a unit square around each visited point. A368000(n)/a(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 A368001 Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.
%H A368001 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%F A368001 A368000(n)/a(n) = (A367994(n)/A367995(n))/A335573(n+1).
%e A368001 As an irregular triangle:
%e A368001      1;
%e A368001      2;
%e A368001      6,  6;
%e A368001     21, 21, 28, 21,   21;
%e A368001   2002, 77, 77, 77, 1001, 77, 77, 1001, 1001, 77, 91, 77;
%e A368001   ...
%Y A368001 Cf. A000105, A246521, A335573, A367676, A367765, A367994, A367995, A368000 (numerators), A368003, A368005.
%K A368001 nonn,frac,tabf
%O A368001 1,2
%A A368001 _Pontus von Brömssen_, Dec 09 2023