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A001412 Number of n-step self-avoiding walks on cubic lattice.
(Formerly M4202 N1754)
+0
10
1, 6, 30, 150, 726, 3534, 16926, 81390, 387966, 1853886, 8809878, 41934150, 198842742, 943974510, 4468911678, 21175146054, 100121875974, 473730252102, 2237723684094, 10576033219614, 49917327838734, 235710090502158, 1111781983442406, 5245988215191414 (list; graph; listen)
OFFSET

0,2

REFERENCES

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

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

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 331-339.

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

A. J. Guttmann, On the critical behavior of self-avoiding walks, J. Phys. A 20 (1987), 1839-1854.

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.

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

D. S. McKenzie and C. Domb, The second osmotic virial coefficient of athermal polymer solutions, Proceedings of the Physical Society, 92 (1967) 632-649.

A. M. Nemirovsky et al., Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108.

M. F. Sykes, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.

M. F. Sykes, Self-avoiding walks on the simple cubic lattice, J. Chem. Phys., 39 (1963), 410-411.

M. F. Sykes et al., The asymptotic behavior of selfavoiding walks and returns on a lattice, J. Phys. A 5 (1972), 653-660.

LINKS

S. R. Finch, Self-Avoiding-Walk Connective Constants

D. Randall, Counting in Lattices: Combinatorial Problems from Statistical Mechanics, PhD Thesis.

N. Clisby, R. Liang and G. Slade Self-avoiding walk enumeration via the lace expansion J. Phys. A: Math. Theor. vol. 40 (2007) p 10973-11017, Table A5 for n<=30.

CROSSREFS

Cf. A002902, A078717, A001411, A001413.

Sequence in context: A002913 A157519 A075886 this_sequence A006818 A006819 A003948

Adjacent sequences: A001409 A001410 A001411 this_sequence A001413 A001414 A001415

KEYWORD

nonn,walk,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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