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

Author

N. J. A. Sloane

Keywords

• nonn
• walk

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

• 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.

Extensions

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