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A001413 Number of 2n-step polygons on cubic lattice.
(Formerly M5154 N2238)
4
0, 24, 264, 3312, 48240, 762096, 12673920, 218904768, 3891176352, 70742410800, 1309643747808, 24609869536800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Counts the number of 2n-step closed self-avoiding paths on the cubic lattice - Bert Dobbelaere, Jan 04 2019

REFERENCES

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 462.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

LINKS

Table of n, a(n) for n=1..12.

M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.

B. J. Hiley and M. F. Sykes, Probability of initial ring closure in the restricted random-walk model of a macromolecule, J. Chem. Phys., 34 (1961), 1531-1537.

M. F. Sykes et al., The number of self-avoiding walks on a lattice, J. Phys. A 5 (1972), 661-666.

CROSSREFS

Cf. A010566 (for square lattice equivalent).

Cf. A002896 (without self-avoidance restriction).

Sequence in context: A000145 A286346 A126904 * A022065 A125412 A270846

Adjacent sequences:  A001410 A001411 A001412 * A001414 A001415 A001416

KEYWORD

nonn,walk,changed

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(11)-a(12) from Bert Dobbelaere, Jan 04 2019

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)