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A006817 Trails of length n on square lattice.
(Formerly M3450)
1
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 (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

Table of n, a(n) for n=0..25.

A. J. Guttmann, Lattice trails II: numerical results, J. Phys. A 22 (1989), 575-588.

CROSSREFS

Undirected trails-rotation and reflection are counted by A001997.

Sequence in context: A290380 A003212 A156945 * A163315 A003119 A001394

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

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.