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A003207 Cluster series for bond percolation problem on cubic lattice.
(Formerly M4708)
7

%I M4708 #16 Feb 02 2022 23:57:23

%S 1,10,50,238,1114,4998,22562,98174,434894,1855346,8125390,34149330

%N Cluster series for bond percolation problem on cubic lattice.

%D 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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. F. Sykes and J. W. Essam, <a href="https://doi.org/10.1103/PhysRev.133.A310">Critical percolation probabilities by series methods</a>, Phys. Rev., 133 (1964), A310-A315.

%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/animals/">Lattice Animals</a>

%H Stephan Mertens and Cristopher Moore, <a href="https://doi.org/10.1088/1751-8121/aae65c">Series expansion of the percolation threshold on hypercubic lattices</a>, J. Phys. A: Math. Theor., 51 (2018), 475001; arXiv:<a href="https://arxiv.org/abs/1805.02701">1805.02701</a> [cond-mat.stat-mech], 2018. See Appendix B.

%Y Cf. A003211 (site percolation), A003198 (square lattice).

%K nonn,more

%O 0,2

%A _N. J. A. Sloane_

%E Name clarified, a(10)-a(11) computed from Mertens & Moore's data added by _Andrey Zabolotskiy_, Feb 02 2022

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)