A006816 -id:A006816 - cp's OEIS frontend

A006814 Related to self-avoiding walks on square lattice.

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

Offset: 1

N. J. A. Sloane

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

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

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.

Cf. A006815, A006816.

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

A006815 Related to self-avoiding walks on square lattice.

Original entry on oeis.org

1, 6, 23, 84, 283, 930, 2921, 9096, 27507, 82930, 244819, 722116, 2096603, 6087290, 17458887, 50090544, 142317089, 404543142

Offset: 1

N. J. A. Sloane

After constructing a self-avoiding walk, bridge together all adjacent neighboring sites on the walk. a(n) is the sum of the lengths of the shortest path in each of the resulting structures from beginning to end (i.e., using the original path and any bridges), across all walks of length n. My attempt to compute this sequence diverges from the listed terms at n=9, for which I get a(9)=27511, a(10)=82938, .... - Sean A. Irvine, Aug 09 2017

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

S. S. Manna, A. J. Guttmann and A. K. Roy, Diffusion on self-avoiding walk networks, J. Phys. A 22 (1989), 3621-3627.

Cf. A006814, A006816.

cp's OEIS Frontend

A006814 Related to self-avoiding walks on square lattice.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions