A366465 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 triangular lattice with periodic boundary conditions.

0, 1, 0, 0, 3, 4, 1, 0, 0, 0, 8, 42, 84, 76, 36, 9, 1, 0, 0, 0, 0, 4, 48, 280, 1008, 2558, 4480, 5088, 3664, 1744, 560, 120, 16, 1, 0, 0, 0, 0, 0, 48, 942, 8679, 49751, 198242, 580910, 1291636, 2219059, 2981241, 3165764, 2687850, 1844733, 1031824, 472021, 176158, 53082, 12650, 2300, 300, 25, 1

Offset

1,5

Links

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

Stephan Mertens, Percolation (Gives first 11 rows)

Example

Triangle begins:
  0, 1,
  0, 0, 2, 3, 1,
  0, 0, 0, 8, 42, 84, 76, 36, 9, 1,
  0, 0, 0, 0, 4, 48, 280, 1008, 2558, 4480, 5088, 3664, 1744, 560, 120, 16, 1,
  0, 0, 0, 0, 0, 48, 942, 8679, 49751, 198242, 580910, 1291636, 2219059, 2981241, 3165764, 2687850, 1844733, 1031824, 472021, 176158, 53082, 12650, 2300, 300, 25, 1,
...

Crossrefs

Cf. A365940-A365957, A366463-A366467.

Sequence in context: A102222 A171657 A287696 * A084301 A195788 A201930

Adjacent sequences: A366462 A366463 A366464 * A366466 A366467 A366468

Keyword

nonn,tabf

Author

N. J. A. Sloane, Oct 12 2023

Status

approved