A003198 Cluster series for bond percolation problem on square lattice.

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

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

• 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 cluster series.
• Index entries for sequences related to square lattice.

Crossrefs

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

Row 6 of A383735.

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