cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A003198 Cluster series for bond percolation problem on square lattice.

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%I A003198 M4118 #25 May 21 2025 09:17:24
%S A003198 1,6,18,48,126,300,762,1668,4216,8668,21988,43058,110832,202432,
%T A003198 561020,875382,2881286,3501056
%N A003198 Cluster series for bond percolation problem on square lattice.
%D A003198 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 A003198 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003198 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 A003198 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 A003198 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 A003198 <a href="/index/Cl#cluster">Index entries for sequences related to cluster series</a>.
%H A003198 <a href="/index/Sq#sqlatt">Index entries for sequences related to square lattice</a>.
%Y A003198 Cf. A003197 (hexagonal), A003199 (honeycomb), A003207 (cubic), A003203 (site percolation).
%Y A003198 Row 6 of A383735.
%K A003198 nonn,more
%O A003198 0,2
%A A003198 _N. J. A. Sloane_
%E A003198 Name clarified, a(12)-a(14) from Sykes & Glen added by _Andrey Zabolotskiy_, Feb 02 2022
%E A003198 a(15)-a(17) from Daboul, Aharony & Stauffer added by _Andrey Zabolotskiy_, Nov 14 2024