A003198 - OEIS

%I M4118 #21 Nov 14 2024 23:49:41

%S 1,6,18,48,126,300,762,1668,4216,8668,21988,43058,110832,202432,

%T 561020,875382,2881286,3501056

%N Cluster series for bond percolation problem on square 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 Daniel Daboul, Amnon Aharony and Dietrich Stauffer, <a href="https://doi.org/10.1088/0305-4470/33/6/303">Universality of amplitude combinations in two-dimensional percolation</a>, J. Phys. A: Math. Gen., 33 (2000), 1113-1137. See Table 1.

%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 M. F. Sykes and M. Glen, <a href="https://doi.org/10.1088/0305-4470/9/1/014">Percolation processes in two dimensions. I. Low-density series expansions</a>, J. Phys. A: Math. Gen., 9 (1976), 87-95.

%H <a href="/index/Sq#sqlatt">Index entries for sequences related to square lattice</a>

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

%K nonn,more

%O 0,2

%A _N. J. A. Sloane_

%E Name clarified, a(12)-a(14) from Sykes & Glen added by _Andrey Zabolotskiy_, Feb 02 2022

%E a(15)-a(17) from Daboul, Aharony & Stauffer added by _Andrey Zabolotskiy_, Nov 14 2024