A006815 Related to self-avoiding walks on square lattice.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• more

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

• 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.