A003207 Cluster series for bond percolation problem on cubic lattice.

1, 10, 50, 238, 1114, 4998, 22562, 98174, 434894, 1855346, 8125390, 34149330

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

• Stephan Mertens, Lattice Animals.
• Stephan Mertens and Cristopher Moore, Series expansion of the percolation threshold on hypercubic lattices, J. Phys. A: Math. Theor., 51 (2018), 475001; arXiv:1805.02701 [cond-mat.stat-mech], 2018. See Appendix B.
• M. F. Sykes and J. W. Essam, Critical percolation probabilities by series methods, Phys. Rev., 133 (1964), A310-A315.
• Index entries for sequences related to cluster series.

Crossrefs

Cf. A003211 (site percolation), A003198 (square lattice).

Row 14 of A383735.

Extensions

Name clarified, a(10)-a(11) computed from Mertens & Moore's data added by Andrey Zabolotskiy, Feb 02 2022