A006836 Percolation series for directed hexagonal lattice. (Formerly M1379)

1, 0, 0, -1, -2, -5, -10, -20, -41, -86, -182, -393, -853, -1887, -4208, -9445, -21350, -48612, -111307, -255236, -590543, -1362919, -3182137, -7362611, -17377129, -40125851, -96106251, -219681825, -539266908, -1200140540

Offset

0,5

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..35 (from link below)

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, 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. A006739.

Sequence in context: A266462 A293319 A267589 * A129847 A330456 A352120

Adjacent sequences: A006833 A006834 A006835 * A006837 A006838 A006839

Keyword

sign

Author

N. J. A. Sloane.

Status

approved