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%I #11 Oct 12 2023 19:24:19
%S 0,1,0,0,6,4,1,0,0,0,9,81,126,84,36,9,1,0,0,0,0,12,240,1704,5824,
%T 10710,11136,8008,4368,1820,560,120,16,1,0,0,0,0,0,15,525,6975,52350,
%U 255875,868195,2098800,3632800,4541775,4286850,3243010,2041200,1081575,480700,177100,53130,12650,2300,300,25,1
%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 triangular lattice with periodic boundary conditions. This is for the probability that it wraps in either dimension.
%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, 9, 81, 126, 84, 36, 9, 1,
%e 0, 0, 0, 0, 12, 240, 1704, 5824, 10710, 11136, 8008, 4368, 1820, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 15, 525, 6975, 52350, 255875, 868195, 2098800, 3632800, 4541775, 4286850, 3243010, 2041200, 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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