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A365940
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 triangular lattice with periodic boundary conditions.
22
0, 1, 0, 4, 7, 4, 1, 0, 9, 45, 90, 126, 126, 84, 36, 9, 1, 0, 16, 192, 1040, 3340, 7104, 10872, 13136, 13500, 11584, 8024, 4368, 1820, 560, 120, 16, 1, 0, 25, 525, 5225, 32725, 144390, 476025, 1214400, 2454525, 4009875, 5420535, 6256650, 6371225, 5810550, 4714050, 3354100, 2064550, 1085475, 481150, 177125, 53130, 12650, 2300, 300, 25, 1
OFFSET
1,4
COMMENTS
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, 7, 4, 1,
0, 9, 45, 90, 126, 126, 84, 36, 9, 1,
0, 16, 192, 1040, 3340, 7104, 10872, 13136, 13500, 11584, 8024, 4368, 1820, 560, 120, 16, 1,
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Oct 09 2023
STATUS
approved