A006816 Related to self-avoiding walks on square lattice. (Formerly M4187)

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

Offset

1,2

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

Table of n, a(n) for n=1..22.

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.

Sequence in context: A164274 A100874 A047923 * A184130 A326805 A061648

Adjacent sequences: A006813 A006814 A006815 * A006817 A006818 A006819

Keyword

nonn,walk

Author

N. J. A. Sloane

Extensions

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

Status

approved