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A365949
Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of exact wrapping probability for site percolation on an n X n 2D square lattice with periodic boundary conditions. This is for the probability that it wraps in both dimensions.
0
0, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 9, 42, 36, 9, 1, 0, 0, 0, 0, 0, 0, 0, 16, 328, 1504, 2960, 2992, 1668, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 1510, 16300, 86925, 285200, 625550, 947740, 1004400, 754775, 412250, 168450, 52620, 12650, 2300, 300, 25, 1
OFFSET
1,6
COMMENTS
The wrapping probability function is Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
LINKS
Stephan Mertens, Percolation (Gives first 7 rows)
EXAMPLE
Triangle begins:
0, 1,
0, 0, 0, 4, 1,
0, 0, 0, 0, 0, 9, 42, 36, 9, 1,
0, 0, 0, 0, 0, 0, 0, 16, 328, 1504, 2960, 2992, 1668, 560, 120, 16, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 1510, 16300, 86925, 285200, 625550, 947740, 1004400, 754775, 412250, 168450, 52620, 12650, 2300, 300, 25, 1,
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Oct 12 2023
STATUS
approved