A003200 Cluster series for site percolation problem on honeycomb matching lattice (honeycomb structure with 1st, 2nd and 3rd neighbors connected). (Formerly M4848)

1, 12, 66, 312, 1368, 5685, 23034, 90288, 350124

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..8.

Keith Malcolm Gwilym, Theory of percolation processes, PhD Thesis, University of London, 1972. See Table 3.1 on p. 55.

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

Crossrefs

Cf. cluster series for site percolation problem: A003201, A003202, A003203, A003204, A003209, A003210, A003211, A003212, A036392, A036394, A036395, A036396, A036397, A036398, A036400, A036401, A036402 and for bond percolation problem: A003197, A003198, A003199, A003205, A003206, A003207, A003208.

Sequence in context: A180392 A161805 A036399 * A353291 A200190 A270251

Adjacent sequences: A003197 A003198 A003199 * A003201 A003202 A003203

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Name clarified by Andrey Zabolotskiy, Mar 04 2021

a(6)-a(8) from Gwilym added by Andrey Zabolotskiy, Apr 13 2023

Status

approved