A366467 - OEIS

A366467

Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of exact spanning probability for site percolation along the second dimension for an n X n 2D nnsquare lattice with periodic boundary conditions.

%I #11 Oct 12 2023 19:27:45

%S 0,1,0,0,4,4,1,0,0,0,17,67,104,81,36,9,1,0,0,0,0,68,632,2594,6168,

%T 9454,9988,7618,4308,1816,560,120,16,1,0,0,0,0,0,259,4351,34162,

%U 165932,556667,1365401,2539513,3682167,4258223,4001349,3098369,1994804,1071617,479282,176976,53125,12650,2300,300,25,1

%N Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of exact spanning probability for site percolation along the second dimension for an n X n 2D nnsquare lattice with periodic boundary conditions.

%C An nnsquare lattice is a square lattice with additional next nearest neighbor links.

%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a> (Gives first 22 rows)

%e Triangle begins:

%e 0, 1,

%e 0, 0, 4, 4, 1,

%e 0, 0, 0, 17, 67, 104, 81, 36, 9, 1,

%e 0, 0, 0, 0, 68, 632, 2594, 6168, 9454, 9988, 7618, 4308, 1816, 560, 120, 16, 1,

%e 0, 0, 0, 0, 0, 259, 4351, 34162, 165932, 556667, 1365401, 2539513, 3682167, 4258223, 4001349, 3098369, 1994804, 1071617, 479282, 176976, 53125, 12650, 2300, 300, 25, 1,

%e ...

%Y Cf. A365940-A365957, A366463-A366466.

%K nonn,tabf

%O 1,5

%A _N. J. A. Sloane_, Oct 12 2023