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.

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, 9454, 9988, 7618, 4308, 1816, 560, 120, 16, 1, 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

Offset

1,5

Comments

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

Links

Table of n, a(n) for n=1..60.

Stephan Mertens, Percolation (Gives first 22 rows)

Example

Triangle begins:
  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, 9454, 9988, 7618, 4308, 1816, 560, 120, 16, 1,
  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,
...

Crossrefs

Cf. A365940-A365957, A366463-A366466.

Sequence in context: A365957 A365954 A260043 * A366464 A185057 A343720

Adjacent sequences: A366464 A366465 A366466 * A366468 A366469 A366470

Keyword

nonn,tabf

Author

N. J. A. Sloane, Oct 12 2023

Status

approved