A003198 Cluster series for bond percolation problem on square lattice. (Formerly M4118)

1, 6, 18, 48, 126, 300, 762, 1668, 4216, 8668, 21988, 43058, 110832, 202432, 561020, 875382, 2881286, 3501056

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..17.

Daniel Daboul, Amnon Aharony and Dietrich Stauffer, Universality of amplitude combinations in two-dimensional percolation, J. Phys. A: Math. Gen., 33 (2000), 1113-1137. 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 square lattice

Crossrefs

Cf. A003197 (hexagonal), A003199 (honeycomb), A003207 (cubic), A003203 (site percolation).

Sequence in context: A256010 A128543 A003202 * A099857 A163765 A179754

Adjacent sequences: A003195 A003196 A003197 * A003199 A003200 A003201

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Name clarified, a(12)-a(14) from Sykes & Glen added by Andrey Zabolotskiy, Feb 02 2022

a(15)-a(17) from Daboul, Aharony & Stauffer added by Andrey Zabolotskiy, Nov 14 2024

Status

approved