A003200
Cluster series for site percolation problem on honeycomb matching lattice (honeycomb structure with 1st, 2nd and 3rd neighbors connected).
Original entry on oeis.org
1, 12, 66, 312, 1368, 5685, 23034, 90288, 350124
Offset: 0
- 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).
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.
A003211
Cluster series for cubic lattice.
Original entry on oeis.org
1, 6, 30, 114, 438, 1542, 5754, 19574, 71958, 233574, 870666, 2696274, 10375770, 30198116, 122634404, 327024444, 1460721616, 3347244554, 17795165832
Offset: 0
- 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).
- 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.
- Index entries for sequences related to cluster series.
A003201
Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected).
Original entry on oeis.org
1, 8, 32, 108, 348, 1068, 3180, 9216, 26452, 73708, 206872, 563200, 1555460, 4124568, 11450284
Offset: 0
- 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).
- 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.
- Index entries for sequences related to cluster series.
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.
A003208
Cluster series for bond percolation problem on diamond.
Original entry on oeis.org
1, 6, 18, 54, 162, 456, 1302, 3630, 10158, 27648, 77022, 206508, 570072, 1521822
Offset: 0
- 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).
Name clarified, a(12)-a(13) from Sykes, Gaunt & Glen added by
Andrey Zabolotskiy, Feb 02 2022
Showing 1-4 of 4 results.