

A010566


Number of 2nstep 2dimensional closed selfavoiding paths on square lattice.
(Formerly N1903)


16



0, 8, 24, 112, 560, 2976, 16464, 94016, 549648, 3273040, 19781168, 121020960, 748039552, 4664263744, 29303071680, 185307690240, 1178635456752, 7535046744864, 48392012257184, 312061600211680, 2019822009608592, 13117263660884768, 85447982919036736
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OFFSET

1,2


COMMENTS

a(n) = 4n*A002931(n). There are (2n) choices for the starting point and 2 choices for the orientation, in order to produce selfavoiding closed paths from a polygon of perimeter 2n.  Philippe Flajolet, Nov 22 2003


REFERENCES

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 461.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).


LINKS

Felix A. Pahl, Table of n, a(n) for n = 1..55 (from Iwan Jensen's computations of A002931, using a(n)=4n*A002931(n))
M. E. Fisher and D. S. Gaunt, Ising model and selfavoiding walks on hypercubical lattices and high density expansions, Phys. Rev. 133 (1964) A224A239.
M. E. Fisher and M. F. Sykes, Excludedvolume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 4558.
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 364.
A. J. Guttmann and I. G. Enting, The size and number of rings on the square lattice, J. Phys. A 21 (1988), L165L172.
Brian Hayes, How to avoid yourself, American Scientist 86 (1998) 314319.
B. J. Hiley and M. F. Sykes, Probability of initial ring closure in the restricted randomwalk model of a macromolecule, J. Chem. Phys., 34 (1961), 15311537.
Iwan Jensen, Series Expansions for SelfAvoiding Walks
G. S. Rushbrooke and J. Eve, On Noncrossing Lattice Polygons, Journal of Chemical Physics, 31 (1959), 13331334.


MATHEMATICA

A002931 = Cases[Import["https://oeis.org/A002931/b002931.txt", "Table"], {_, _}][[All, 2]]; a[n_] := 4n A002931[[n]];
a /@ Range[55] (* JeanFrançois Alcover, Jan 11 2020 *)


CROSSREFS

Cf. A002931.
Sequence in context: A063515 A220706 A246030 * A305224 A182068 A092771
Adjacent sequences: A010563 A010564 A010565 * A010567 A010568 A010569


KEYWORD

nonn,nice,walk


AUTHOR

N. J. A. Sloane


STATUS

approved



