OFFSET
1,3
COMMENTS
In internal diffusion-limited aggregation on the square lattice, there is one initial cell in the origin. In each subsequent step, a new cell is added by starting a random walk at the origin, adding the first new cell visited. a(n)/A368387(n) is the probability that, when the appropriate number of cells have been added, those cells form the free polyomino with binary code A246521(n+1).
Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 1..6473 (rows 1..10).
Persi Diaconis and William Fulton, A growth model, a game, an algebra, Lagrange inversion, and characteristic classes, Rend. Semin. Mat. Univ. Politec. Torino, Vol. 49 (1991), No. 1, 95-119.
Gregory F. Lawler, Maury Bramson, and David Griffeath, Internal diffusion limited aggregation, The Annals of Probability 20 no. 4 (1992), 2117-2140.
EXAMPLE
As an irregular triangle:
1;
1;
2, 1;
8, 4, 17, 4, 2;
57, 5, 5, 5, 73, 5, 5, 73, 73, 5, 1, 5;
...
There are only one monomino and one free domino, so both of these appear with probability 1, and a(1) = a(2) = 1.
CROSSREFS
KEYWORD
nonn,frac,tabf
AUTHOR
Pontus von Brömssen, Dec 22 2023
STATUS
approved