A367995 a(n) is the denominator 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.
1, 1, 3, 3, 21, 21, 7, 21, 21, 1001, 77, 77, 77, 1001, 77, 77, 1001, 1001, 77, 91, 77, 89089, 785603, 143, 143, 24297, 143, 25924899, 97097, 785603, 97097, 25924899, 143, 89089, 143, 97097, 97097, 143, 25924899, 97097, 97097, 143, 143, 97097, 143, 97097, 143, 143, 97097, 97097, 97097, 143, 97097, 291291, 291291, 143
Offset: 1
Examples
As an irregular triangle:
1;
1;
3, 3;
21, 21, 7, 21, 21;
1001, 77, 77, 77, 1001, 77, 77, 1001, 1001, 77, 91, 77;
...
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) = 3. The probability for the straight tromino (whose binary code is 11 = A246521(5)) is 1/3, so a(4) = 3.
Links
- Pontus von Brömssen, Table of n, a(n) for n = 1..6473 (rows 1..10).
- Index entries for sequences related to polyominoes.
Comments