A003207 Cluster series for bond percolation problem on cubic lattice. (Formerly M4708)

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

Offset

0,2

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..11.

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.

Sequence in context: A201830 A192019 A201210 * A095687 A204272 A220149

Adjacent sequences: A003204 A003205 A003206 * A003208 A003209 A003210

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

Status

approved