A003201 Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected). (Formerly M4510)

1, 8, 32, 108, 348, 1068, 3180, 9216, 26452, 73708, 206872, 563200, 1555460, 4124568, 11450284

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..14.

S. Mertens, Lattice animals: a fast enumeration algorithm and new perimeter polynomials, J. Stat. Phys. 58 (1990) 1095-1108 (Table II, column nnSquare).

M. F. Sykes and J. W. Essam, Critical percolation probabilities by series methods, Phys. Rev., 133 (1964), A310-A315.

M. F. Sykes and Sylvia Flesia, Lattice animals: Supplementation of perimeter polynomial data by graph-theoretic methods, Journal of Statistical Physics, 63 (1991), 487-489.

Crossrefs

Cf. cluster series for site percolation problem: A003200, A003202, A003203, A003204, A003209, A003210, A003211, A003212, A036392, A036394-A036402 and for bond percolation problem: A003197, A003198, A003199, A003205, A003206, A003207, A003208.

Sequence in context: A302507 A204643 A036393 * A318944 A196097 A234272

Adjacent sequences: A003198 A003199 A003200 * A003202 A003203 A003204

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Name clarified by Andrey Zabolotskiy, Mar 04 2021

a(8)-a(13) from Mertens added by Andrey Zabolotskiy, Feb 01 2022

a(14) from Sykes & Flesia added by Andrey Zabolotskiy, Jan 28 2023

Status

approved