A003197 Cluster series for bond percolation problem on hexagonal lattice.

1, 10, 46, 186, 706, 2568, 9004, 30894, 103832, 343006, 1123770, 3623234, 11630150

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
• D. F. Styer, M. D. Edwards and E. A. Andrews, The size function in two-dimensional bond percolation: a series analysis, J. Phys. A: Math. Gen., 21 (1988), L1153-L1156. See Table 1.
• 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).

Extensions

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

a(11)-a(12) from Styer, Edwards & Andrews added by Andrey Zabolotskiy, Nov 14 2024