A006815 Related to self-avoiding walks on square lattice. (Formerly M4157)

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

Offset

1,2

Comments

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

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..18.

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. A006814, A006816.

Sequence in context: A220238 A078798 A027043 * A264690 A241394 A054491

Adjacent sequences: A006812 A006813 A006814 * A006816 A006817 A006818

Keyword

nonn,walk,more

Author

N. J. A. Sloane

Status

approved