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A001413 Number of 2n-step polygons on cubic lattice.
(Formerly M5154 N2238)
7
0, 24, 264, 3312, 48240, 762096, 12673920, 218904768, 3891176352, 70742410800, 1309643747808, 24609869536800, 468270744898944, 9005391024862848, 174776445357365040, 3419171337633496704 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is 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
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, D. S. McKenzie, M. G. Watts, and J. L. Martin, The number of self-avoiding walks on a lattice, J. Phys. A 5 (1972), 661-666.
FORMULA
a(n) = 4*n*A001409(n). - Sean A. Irvine, Jul 27 2020
CROSSREFS
Cf. A001409.
Cf. A010566 (for square lattice equivalent).
Cf. A002896 (without self-avoidance restriction).
Sequence in context: A000145 A286346 A126904 * A022065 A125412 A270846
KEYWORD
nonn,walk,more
AUTHOR
EXTENSIONS
a(11)-a(12) from Bert Dobbelaere, Jan 04 2019
a(13)-a(16) (using A001409) from Alois P. Heinz, Feb 28 2024
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)