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A365942
Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of cluster density function for site percolation on an n X n 2D nnsquare lattice with periodic boundary conditions.
1
0, 1, 0, 4, 6, 4, 1, 0, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 16, 176, 848, 2448, 5056, 8440, 11584, 12890, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 25, 500, 4700, 27500, 112145, 339650, 801500, 1543750, 2538800, 3675220, 4717300, 5330625, 5250975, 4472200, 3271820, 2043375, 1081600, 480700, 177100, 53130, 12650, 2300, 300, 25, 1
OFFSET
1,4
COMMENTS
An nnsquare lattice is a square lattice with additional next nearest neighbor links.
The cluster density function is (1/n^2)*Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
REFERENCES
S. Mertens, I. Jensen, and R. M. Ziff, Universal features of cluster numbers in percolation, Physical Review E 96 (2017) 052119.
LINKS
Stephan Mertens, Percolation (Gives first 7 rows)
EXAMPLE
Triangle begins:
0, 1,
0, 4, 6, 4, 1,
0, 9, 36, 84, 126, 126, 84, 36, 9, 1,
0, 16, 176, 848, 2448, 5056, 8440, 11584, 12890, 11440, 8008, 4368, 1820, 560, 120, 16, 1,
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Oct 09 2023
STATUS
approved