cp's OEIS Frontend

A003201 Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected).

%I A003201 M4510 #33 May 21 2025 09:21:20
%S A003201 1,8,32,108,348,1068,3180,9216,26452,73708,206872,563200,1555460,
%T A003201 4124568,11450284
%N A003201 Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected).
%D A003201 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 A003201 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003201 S. Mertens, <a href="https://doi.org/10.1007/BF01026565">Lattice animals: a fast enumeration algorithm and new perimeter polynomials</a>, J. Stat. Phys. 58 (1990) 1095-1108 (Table II, column nnSquare).
%H A003201 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 A003201 M. F. Sykes and Sylvia Flesia, <a href="https://doi.org/10.1007/BF01029196">Lattice animals: Supplementation of perimeter polynomial data by graph-theoretic methods</a>, Journal of Statistical Physics, 63 (1991), 487-489.
%H A003201 <a href="/index/Cl#cluster">Index entries for sequences related to cluster series</a>.
%Y A003201 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.
%Y A003201 Row 10 of A383735.
%K A003201 nonn,more
%O A003201 0,2
%A A003201 _N. J. A. Sloane_
%E A003201 Name clarified by _Andrey Zabolotskiy_, Mar 04 2021
%E A003201 a(8)-a(13) from Mertens added by _Andrey Zabolotskiy_, Feb 01 2022
%E A003201 a(14) from Sykes & Flesia added by _Andrey Zabolotskiy_, Jan 28 2023