A006803 Percolation series for hexagonal lattice. (Formerly M2232)

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

0,6

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.

Sequence in context: A185580 A052931 A368379 * A197730 A231902 A143495

Adjacent sequences: A006800 A006801 A006802 * A006804 A006805 A006806

Keyword

sign

Author

N. J. A. Sloane

Status

approved