|
%I #10 Jan 10 2024 23:55:10
%S 1,0,0,0,5,0,0,0,1,0,0,0,4,2,0,0,0,3,1,0,0,0,0,1,3,5,0,0,0,0,7,6,3,5,
%T 0,0,0,0,1,5,3,4,5,0,0,0,0,8,6,1,6,1,3,0,0,0,0,7,2,1,2,0,7,8,0,0,0,0,
%U 2,5,7,9,7,9,1,1,0,0,0,0,2,5,4,4,5,4,3,6,1,0,0
%N Square array read by antidiagonals; the n-th row is the decimal expansion 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 in diffusion-limited aggregation on the square lattice.
%C The n-th row is the decimal expansion of the number on the n-th row of A368660 divided by A335573(n+1). See A368660 for details.
%C Rows A130866(k-1)+1 to A130866(k) correspond to k-celled polyominoes, k >= 2.
%H Pontus von Brömssen, <a href="/A368863/b368863.txt">Table of n, a(n) for n = 1..1596</a> (first 56 antidiagonals).
%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%e Array begins:
%e 1.00000000000000000000... (monomino)
%e 0.50000000000000000000... (domino)
%e 0.14317187227209462175... (L tromino)
%e 0.21365625545581075649... (I tromino)
%e 0.05331174468766310877... (L tetromino)
%e 0.05462942885357382723... (square tetromino)
%e 0.05107523273680265528... (T tetromino)
%e 0.03794485956843370668... (S tetromino)
%e 0.08139812221208792734... (I tetromino)
%e 0.01652391644265825925... (P pentomino)
%e 0.01709341200261444870... (V pentomino)
%e 0.00933365290110550590... (W pentomino)
%e 0.01825698429438352158... (L pentomino)
%e 0.01973313069852314774... (Y pentomino)
%e 0.01316184592639931744... (N pentomino)
%e 0.01069856796007681265... (U pentomino)
%e 0.02067501830899727807... (T pentomino)
%e 0.01358243200363682514... (F pentomino)
%e 0.01232428737930631004... (Z pentomino)
%e 0.01279646275569121440... (X pentomino)
%e 0.02831865405554939733... (I pentomino)
%e ...
%Y Cf. A000105, A001168, A130866, A246521, A335573, A368660 (free polyominoes), A368864, A368865.
%Y Corresponding sequences for internal diffusion-limited aggregation: A368392, A368393.
%K nonn,tabl,cons
%O 1,5
%A _Pontus von Brömssen_, Jan 08 2024
|
