A006817 Trails of length n on square lattice. (Formerly M3450)

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

0,2

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.

Sequence in context: A290380 A003212 A156945 * A163315 A326339 A334877

Adjacent sequences: A006814 A006815 A006816 * A006818 A006819 A006820

Keyword

nonn,walk

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson, Jul 20 2001

More terms from Bert Dobbelaere, Jan 19 2019

Status

approved