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A006817 Trails of length n on square lattice.
(Formerly M3450)
2
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 (list; graph; refs; listen; history; text; internal format)
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.
Sequence in context: A290380 A003212 A156945 * A163315 A326339 A334877
KEYWORD
nonn,walk
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Jul 20 2001
More terms from Bert Dobbelaere, Jan 19 2019
STATUS
approved

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Last modified February 26 01:57 EST 2024. Contains 370335 sequences. (Running on oeis4.)