A003197 Cluster series for bond percolation problem on hexagonal lattice. (Formerly M4705)

1, 10, 46, 186, 706, 2568, 9004, 30894, 103832, 343006, 1123770

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.

References

J. W. Essam, Percolation and cluster size, in C. Domb and M. S. Green, Phase Transitions and Critical Phenomena, Ac. Press 1972, Vol. 2; see especially pp. 225-226.

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

Links

Table of n, a(n) for n=0..10.

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

M. F. Sykes and J. W. Essam, Critical percolation probabilities by series methods, Phys. Rev., 133 (1964), A310-A315.

M. F. Sykes and M. Glen, Percolation processes in two dimensions. I. Low-density series expansions, J. Phys. A: Math. Gen., 9 (1976), 87-95.

Index entries for sequences related to A2 = hexagonal = triangular lattice

Crossrefs

Cf. A003198 (square), A003199 (honeycomb), A003202 (site percolation).

Sequence in context: A024166 A103501 A219003 * A096045 A287090 A183133

Adjacent sequences: A003194 A003195 A003196 * A003198 A003199 A003200

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Name clarified, a(10) from Sykes & Glen added by Andrey Zabolotskiy, Feb 02 2022

Status

approved