A006817 Trails of length n on square lattice.

1, 4, 12, 36, 108, 316, 916, 2628, 7500, 21268, 60092, 169092, 474924, 1329188, 3715244, 10359636, 28856252, 80220244, 222847804, 618083972, 1713283628, 4742946484, 13123882524, 36274940740, 100226653420, 276669062116, 763482430316, 2105208491748, 5803285527724

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk

Comments

A trail is a path which may cross itself but does not reuse an edge. This sequence counts directed paths on the square lattice.

References

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

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 0..31 (from Conway & Guttmann; terms 0..30 from Bert Dobbelaere)
• A. R. Conway and A. J. Guttmann, Enumeration of self-avoiding trails on a square lattice using a transfer matrix technique, J. Phys. A: Math. Gen., 26 (1993), 1535-1552; arXiv:hep-lat/9211063, 1992.
• A. J. Guttmann, Lattice trails II: numerical results, J. Phys. A 22 (1989), 575-588.
• A. Malakis, The trail problem on the square lattice, J. Phys A 9 (8) (1976) p 1283. Table 1.

Crossrefs

Undirected trails-rotation and reflection are counted by A001997.

Cf. A006818, A006819, A006851.

Extensions

More terms from David W. Wilson, Jul 20 2001

More terms from Bert Dobbelaere, Jan 19 2019