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A002902
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Number of n-step self-avoiding walks on a cubic lattice with a first step along the positive x, y, or z axis.
(Formerly M2990 N1210)
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5
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3, 15, 75, 363, 1767, 8463, 40695, 193983, 926943, 4404939, 20967075, 99421371, 471987255, 2234455839, 10587573027, 50060937987, 236865126051, 1118861842047, 5288016609807, 24958663919367, 117855045251079, 555890991721203, 2622994107595707
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OFFSET
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1,1
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..23.
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, 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.
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CROSSREFS
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Equals (1/2)*A001412. Cf. A078717, A001411, A001413.
Sequence in context: A190010 A151326 A063000 * A236579 A005053 A329764
Adjacent sequences: A002899 A002900 A002901 * A002903 A002904 A002905
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KEYWORD
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nonn,walk,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Name amended by Scott R. Shannon, Sep 17 2020
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STATUS
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approved
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