A002902 Number of n-step self-avoiding walks on a cubic lattice with a first step along the positive x, y, or z axis.

3, 15, 75, 363, 1767, 8463, 40695, 193983, 926943, 4404939, 20967075, 99421371, 471987255, 2234455839, 10587573027, 50060937987, 236865126051, 1118861842047, 5288016609807, 24958663919367, 117855045251079, 555890991721203, 2622994107595707

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• nice

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

• 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.

Crossrefs

Equals (1/2)*A001412. Cf. A078717, A001411, A001413.

Extensions

Name amended by Scott R. Shannon, Sep 17 2020