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A001412 Number of n-step self-avoiding walks on cubic lattice.
(Formerly M4202 N1754)
1, 6, 30, 150, 726, 3534, 16926, 81390, 387966, 1853886, 8809878, 41934150, 198842742, 943974510, 4468911678, 21175146054, 100121875974, 473730252102, 2237723684094, 10576033219614, 49917327838734, 235710090502158, 1111781983442406, 5245988215191414, 24730180885580790, 116618841700433358, 549493796867100942, 2589874864863200574, 12198184788179866902, 57466913094951837030, 270569905525454674614 (list; graph; refs; listen; history; text; internal format)



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.

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).

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.


R. D. Schram, G. T. Barkema, R. H. Bisseling, Table of n, a(n) for n = 0..36

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.

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

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

Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling, Exact enumeration of self-avoiding walks, Apr 12, 2011 [Jonathan Vos Post, Apr 13 2011]


Cf. A002902, A078717, A001411, A001413.

Sequence in context: A002913 A157519 A075886 * A162937 A006818 A006819

Adjacent sequences:  A001409 A001410 A001411 * A001413 A001414 A001415




N. J. A. Sloane



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Last modified November 18 12:21 EST 2017. Contains 294891 sequences.