|
%I #15 Oct 12 2023 19:23:19
%S 0,1,0,0,2,4,1,0,0,0,6,45,90,78,36,9,1,0,0,0,0,8,160,1240,4400,8202,
%T 9440,7448,4272,1812,560,120,16,1,0,0,0,0,0,10,350,5350,45550,238925,
%U 819740,1915800,3190350,3977875,3879550,3055790,1982350,1068575,478700,176900,53120,12650,2300,300,25,1
%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 both dimensions.
%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, 2, 4, 1,
%e 0, 0, 0, 6, 45, 90, 78, 36, 9, 1,
%e 0, 0, 0, 0, 8, 160, 1240, 4400, 8202, 9440, 7448, 4272, 1812, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 10, 350, 5350, 45550, 238925, 819740, 1915800, 3190350, 3977875, 3879550, 3055790, 1982350, 1068575, 478700, 176900, 53120, 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
|
