A006809 Bond percolation series for hexagonal lattice. (Formerly M2796 M2797)

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

0,2

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.

Sequence in context: A335472 A096322 A058396 * A081663 A245748 A181383

Adjacent sequences: A006806 A006807 A006808 * A006810 A006811 A006812

Keyword

sign

Author

N. J. A. Sloane, Simon Plouffe

Status

approved