|
|
A367994
|
|
a(n) is the numerator of the probability that the free polyomino with binary code A246521(n+1) appears as the image of a simple random walk on the square lattice.
|
|
9
|
|
|
1, 1, 2, 1, 8, 4, 1, 4, 2, 388, 4, 4, 8, 64, 8, 4, 32, 64, 4, 1, 2, 3468, 76520, 4, 4, 2495, 4, 2102248, 1556, 76520, 1556, 1051124, 4, 3468, 4, 1194, 1556, 4, 1262762, 597, 1556, 2, 4, 1556, 4, 597, 2, 2, 778, 1194, 1556, 2, 1194, 2501, 1648, 1, 5270, 13652575732976, 13652575732976, 4468, 4468
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
In a simple random walk on the square lattice, draw a unit square around each visited point. a(n)/A367995(n) is the probability that, when the appropriate number of distinct points have been visited, the drawn squares 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
|
|
|
FORMULA
|
|
|
EXAMPLE
|
As an irregular triangle:
1;
1;
2, 1;
8, 4, 1, 4, 2;
388, 4, 4, 8, 64, 8, 4, 32, 64, 4, 1, 2;
...
There are only one monomino and one free domino, so both of these appear with probability 1, and a(1) = a(2) = 1.
For three squares, the probability for an L (or right) tromino (whose binary code is 7 = A246521(4)) is 2/3, so a(3) = 2. The probability for the straight tromino (whose binary code is 11 = A246521(5)) is 1/3, so a(4) = 1.
|
|
CROSSREFS
|
Cf. A000105, A246521, A335573, A367671, A367760, A367995 (denominators), A367996, A367998, A368000, A368001, A368386.
|
|
KEYWORD
|
nonn,frac,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|