A006809 Bond percolation series for hexagonal lattice.

1, 3, 9, 25, 66, 168, 417, 1014, 2427, 5737, 13412, 31088, 71506, 163378, 371272, 839248, 1889019, 4235082, 9459687, 21067566, 46769977, 103574916, 228808544, 504286803, 1109344029, 2435398781, 5337497418, 11678931098

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• sign

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

The first negative term occurs at index 89.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• I. Jensen, Table of n, a(n) for n = 0..90 (from link below)
• J. Blease, Series expansions for the directed-bond percolation problem, J. Phys. C 10 (1977), 917-924.
• J. W. Essam, A. J. Guttmann and K. De'Bell, On two-dimensional directed percolation, J. Phys. A 21 (1988), 3815-3832.
• I. Jensen, More terms
• Iwan Jensen, Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, J. Phys. A 28 (1995), no. 17, 4813-4833.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Crossrefs

Cf. A006803, A006736.