%I M2796 M2797 #26 Feb 10 2024 09:23:47

%S 1,3,9,25,66,168,417,1014,2427,5737,13412,31088,71506,163378,371272,

%T 839248,1889019,4235082,9459687,21067566,46769977,103574916,228808544,

%U 504286803,1109344029,2435398781,5337497418,11678931098

%N Bond percolation series for hexagonal lattice.

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

%C The first negative term occurs at index 89.

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

%H I. Jensen, <a href="/A006809/b006809.txt">Table of n, a(n) for n = 0..90</a> (from link below)

%H J. Blease, <a href="http://dx.doi.org/10.1088/0022-3719/10/7/003">Series expansions for the directed-bond percolation problem</a>, J. Phys. C 10 (1977), 917-924.

%H J. W. Essam, A. J. Guttmann and K. De'Bell, <a href="http://dx.doi.org/10.1088/0305-4470/21/19/018">On two-dimensional directed percolation</a>, J. Phys. A 21 (1988), 3815-3832.

%H I. Jensen, <a href="https://web.archive.org/web/20160102114433/http://www.ms.unimelb.edu.au/%7Eiwan/dirperc/series/triabond_cs.ser">More terms</a>

%H Iwan Jensen, Anthony J. Guttmann, <a href="http://arxiv.org/abs/cond-mat/9509121">Series expansions of the percolation probability for directed square and honeycomb lattices</a>, J. Phys. A 28 (1995), no. 17, 4813-4833.

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>

%Y Cf. A006803, A006736.

%K sign

%O 0,2

%A _N. J. A. Sloane_, _Simon Plouffe_