A003211 - OEIS

A003211

Cluster series for cubic lattice.
(Formerly M4192)

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

(list; graph; refs; listen; history; text; internal format)

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..18.

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.

CROSSREFS

Cf. A003209 (f.c.c.), A003210 (b.c.c.), A003212 (diamond), A003207 (bond percolation).

Sequence in context: A225382 A245804 A292296 * A334331 A117489 A050510

Adjacent sequences: A003208 A003209 A003210 * A003212 A003213 A003214

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane

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

STATUS

approved