A006729 - OEIS

%I M2088 #25 Oct 05 2019 09:15:12

%S 2,16,72,252,764,2094,5362,12968,30138,67446,147048,311940,649860,

%T 1325234,2668130,5278066,10346200,19977010,38329556,72546986,

%U 136785444,254596418,473093498,868060738,1593517724

%N Series for second parallel moment of square lattice (eventually changes sign).

%C The first negative term is the 70th.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H I. Jensen, <a href="/A006729/b006729.txt">Table of n, a(n) for n = 0..170</a> (from Jensen link below)

%H I. G. Enting, A, J. Guttmann and I. Jensen, <a href="https://arxiv.org/abs/hep-lat/9410005">Low-Temperature Series Expansions for the Spin-1 Ising Model</a>, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7006.

%H J. W. Essam et al., <a href="http://dx.doi.org/10.1103/PhysRevB.33.1982">Analysis of extended series for bond percolation on the directed square lattice</a>, Phys. Rev. B 33 (1986), 1982-1986.

%H J. W. Essam, A. J. Guttmann and K. De'Bell, <a href="http://dx.doi.org/10.1088/0305-4470/21/19/018">On two-dimensional directed percolation</a>, J. Phys. A 21 (1988), 3815-3832.

%H I. Jensen, <a href="https://researchers.ms.unimelb.edu.au/~ij@unimelb/dirperc/series/sqbt2.ser">More terms</a>

%H Iwan Jensen, Anthony J. Guttmann, <a href="http://arxiv.org/abs/cond-mat/9509121">Series expansions of the percolation probability for directed square and honeycomb lattices</a>, J. Phys. A 28 (1995), no. 17, 4813-4833.

%Y Cf. A006461, A006727, A006728, A006730, A260330.

%K sign

%O 0,1

%A _N. J. A. Sloane_, _Simon Plouffe_