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A324603 Number of non-intersecting loops starting at (0,0) on the n X n torus consisting of steps up and to the right. 1
2, 4, 22, 258, 3528, 87830, 8295536 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

On the 2 X 2 torus, the 4 walks are:

[(0,0),(1,0),(0,0)]

[(0,0),(0,1),(0,0)]

[(0,0),(0,1),(1,1),(1,0),(0,0)]

[(0,0),(1,0),(1,1),(0,1),(0,0)]

On the 3 X 3 torus, the 22 walks are all equivalent to the following eleven walks by switching coordinates:

[(0,0),(0,1),(0,2),(0,0)]

[(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(0,0)]

[(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),(0,0)]

[(0,0),(0,1),(1,1),(1,2),(2,2),(0,2),(0,0)]

[(0,0),(0,1),(1,1),(1,2),(2,2),(2,0),(0,0)]

[(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(0,0)]

[(0,0),(0,1),(0,2),(1,2),(2,2),(2,0),(0,0)]

[(0,0),(0,1),(0,2),(1,2),(1,0),(2,0),(0,0)]

[(0,0),(0,1),(1,1),(2,1),(2,2),(0,2),(1,2),(1,0),(2,0),(0,0)]

[(0,0),(0,1),(1,1),(1,2),(1,0),(2,0),(2,1),(2,2),(0,2),(0,0)]

[(0,0),(0,1),(0,2),(1,2),(1,0),(1,1),(2,1),(2,2),(2,0),(0,0]]

LINKS

Table of n, a(n) for n=1..7.

Peter Kagey, Cycles on the torus, Programming Puzzles & Code Golf Stack Exchange.

CROSSREFS

Cf. A000984, A324604.

Sequence in context: A019025 A264729 A192332 * A322520 A018279 A307459

Adjacent sequences:  A324600 A324601 A324602 * A324604 A324605 A324606

KEYWORD

nonn,more,walk

AUTHOR

Peter Kagey, Mar 09 2019

STATUS

approved

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)