%I M4117 #34 Jan 28 2023 15:47:18
%S 1,6,18,48,126,300,750,1686,4074,8868,20892,44634,103392,216348,
%T 499908,1017780,2383596,4648470,11271102,20763036,52671018,91377918
%N Cluster series for hexagonal lattice.
%C The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular 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 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.
%H Stephan Mertens and Markus E. Lautenbacher, <a href="https://doi.org/10.1007/BF01060088">Counting lattice animals: A parallel attack</a>, J. Stat. Phys., 66 (1992), 669-678.
%H 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 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 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 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.
%Y Cf. A003203 (square net), A003204 (honeycomb net), A003197 (bond percolation).
%K nonn,more
%O 0,2
%A _N. J. A. Sloane_
%E a(10)-a(11) from _Sean A. Irvine_, Aug 16 2020
%E a(12)-a(18) added from Mertens by _Andrey Zabolotskiy_, Feb 01 2022
%E a(19)-a(21) from Mertens & Lautenbacher added by _Andrey Zabolotskiy_, Jan 28 2023