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A002902 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)
3, 15, 75, 363, 1767, 8463, 40695, 193983, 926943, 4404939, 20967075, 99421371, 471987255, 2234455839, 10587573027, 50060937987, 236865126051, 1118861842047, 5288016609807, 24958663919367, 117855045251079, 555890991721203, 2622994107595707 (list; graph; refs; listen; history; text; internal format)



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).


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.


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




N. J. A. Sloane.


Name amended by Scott R. Shannon, Sep 17 2020



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Last modified April 15 09:32 EDT 2021. Contains 342977 sequences. (Running on oeis4.)