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%I #9 Oct 12 2023 19:26:37
%S 0,1,0,0,4,4,1,0,0,0,27,81,108,81,36,9,1,0,0,0,0,84,832,3368,7376,
%T 10432,10432,7728,4320,1816,560,120,16,1,0,0,0,0,0,265,4675,39300,
%U 201000,687425,1660325,2970175,4114225,4569025,4165275,3161975,2012650,1075075,479700,177000,53125,12650,2300,300,25,1
%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 around the vertical 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, 4, 4, 1,
%e 0, 0, 0, 27, 81, 108, 81, 36, 9, 1,
%e 0, 0, 0, 0, 84, 832, 3368, 7376, 10432, 10432, 7728, 4320, 1816, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 265, 4675, 39300, 201000, 687425, 1660325, 2970175, 4114225, 4569025, 4165275, 3161975, 2012650, 1075075, 479700, 177000, 53125, 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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