A006814 Related to self-avoiding walks on square lattice. (Formerly M4145)

1, 6, 21, 76, 249, 814, 2521, 7824, 23473, 70590, 207345, 610356, 1765959, 511006, 14643993, 41958852, 118976633, 337823486, 951157365, 2681163492, 7505218171, 21030311474

Offset

1,2

Comments

After constructing a self-avoiding walk, bridge together all adjacent neighboring sites on the walk. Then imagine a current flowing through the resulting structure. This sequence is the sum of the number of links carrying the full current across all walks of length n. - Sean A. Irvine, Aug 08 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)

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. A006815, A006816.

Sequence in context: A200249 A207097 A027281 * A108136 A054625 A192733

Adjacent sequences: A006811 A006812 A006813 * A006815 A006816 A006817

Keyword

nonn,walk

Author

N. J. A. Sloane

Extensions

a(19)-a(22) from Sean A. Irvine, Aug 08 2017

Status

approved