A006816 Related to self-avoiding walks on square lattice.

1, 6, 29, 108, 393, 1298, 4271, 13312, 41469, 125042, 376747, 1111144, 3274475, 9505054, 27573041, 79086964, 226727667, 644301026, 1830188555, 5162408200, 14556754485, 40811281170

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk

Comments

After constructing a self-avoiding walk, bridge together all adjacent neighboring sites on the walk. This sequence is sum of the total number of links after adding bridges across all walks of length n. - Sean A. Irvine, Aug 09 2017

References

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

Links

• A. J. Guttmann and J. Wang, The extension of self-avoiding random walk series in 2 dimensions, Preprint. (Annotated scanned copy)
• B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, Tables and references for self-avoiding walks counts [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The self-avoiding walk"]
• S. S. Manna, A. J. Guttmann and A. K. Roy, Diffusion on self-avoiding walk networks, J. Phys. A 22 (1989), 3621-3627.

Crossrefs

Cf. A001411, A006814, A006815.

Extensions

a(19)-a(22) from Sean A. Irvine, Aug 09 2017