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A003197 Cluster series for bond percolation problem on hexagonal lattice.

%I A003197 M4705 #23 Nov 14 2024 23:49:59
%S A003197 1,10,46,186,706,2568,9004,30894,103832,343006,1123770,3623234,
%T A003197 11630150
%N A003197 Cluster series for bond percolation problem on hexagonal lattice.
%C A003197 The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
%D A003197 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 A003197 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003197 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>
%H A003197 D. F. Styer, M. D. Edwards and E. A. Andrews, <a href="https://doi.org/10.1088/0305-4470/21/23/009">The size function in two-dimensional bond percolation: a series analysis</a>, J. Phys. A: Math. Gen., 21 (1988), L1153-L1156. See Table 1.
%H A003197 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 A003197 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 A003197 <a href="/index/Aa#A2">Index entries for sequences related to A2 = hexagonal = triangular lattice</a>
%Y A003197 Cf. A003198 (square), A003199 (honeycomb), A003202 (site percolation).
%K A003197 nonn,more
%O A003197 0,2
%A A003197 _N. J. A. Sloane_
%E A003197 Name clarified, a(10) from Sykes & Glen added by _Andrey Zabolotskiy_, Feb 02 2022
%E A003197 a(11)-a(12) from Styer, Edwards & Andrews added by _Andrey Zabolotskiy_, Nov 14 2024