A006803 Percolation series for hexagonal lattice.

1, 0, 0, -1, 0, -3, 1, -9, 6, -29, 27, -99, 112, -351, 450, -1275, 1782, -4704, 6998, -17531, 27324, -65758, 106211, -247669, 411291, -935107, 1587391, -3535398, 6108103, -13373929, 23438144, -50592067, 89703467, -191306745, 342473589

Offset: 0

Author

N. J. A. Sloane

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.

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..51
• J. Blease, Series expansions for the directed-bond percolation problem, J. Phys C vol 10 no 7 (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 and Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, arXiv:cond-mat/9509121, 1995; 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. A006809.