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%I #11 Oct 12 2023 19:24:54
%S 0,1,0,0,6,4,1,0,0,0,48,117,126,84,36,9,1,0,0,0,0,160,1504,5496,10352,
%T 12662,11424,8008,4368,1820,560,120,16,1,0,0,0,0,0,520,9000,73250,
%U 356450,1135925,2500910,4024550,5038100,5160175,4451000,3268160,2042950,1081575,480700,177100,53130,12650,2300,300,25,1
%N 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 nnsquare lattice with periodic boundary conditions. This is for the probability that it wraps in either dimension.
%C An nnsquare lattice is a square lattice with additional next nearest neighbor links.
%C The wrapping probability function is Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a> (Gives first 7 rows)
%e Triangle begins:
%e 0, 1,
%e 0, 0, 6, 4, 1,
%e 0, 0, 0, 48, 117, 126, 84, 36, 9, 1,
%e 0, 0, 0, 0, 160, 1504, 5496, 10352, 12662, 11424, 8008, 4368, 1820, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 520, 9000, 73250, 356450, 1135925, 2500910, 4024550, 5038100, 5160175, 4451000, 3268160, 2042950, 1081575, 480700, 177100, 53130, 12650, 2300, 300, 25, 1,
%e ...
%Y Cf. A365940-A365957, A366463-A366467.
%K nonn,tabf
%O 1,5
%A _N. J. A. Sloane_, Oct 12 2023
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