A003211 Cluster series for cubic lattice.

1, 6, 30, 114, 438, 1542, 5754, 19574, 71958, 233574, 870666, 2696274, 10375770, 30198116, 122634404, 327024444, 1460721616, 3347244554, 17795165832

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

• John Adler, Series Expansions, Computers in Physics, 8 (1994), 287-295.
• S. Luther and S. Mertens, Counting lattice animals in high dimensions, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565; arXiv:1106.1078 [cond-mat.stat-mech], 2011. See Table 5.
• Stephan Mertens, Lattice Animals
• 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. A003209 (f.c.c.), A003210 (b.c.c.), A003212 (diamond), A003207 (bond percolation).

Row 32 of A383735.

Extensions

a(9)-a(12) from Sean A. Irvine, Aug 19 2020

a(13)-a(18) from Luther & Mertens added by Andrey Zabolotskiy, Feb 02 2022