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A200000 Number of meanders filling out an n-by-n grid, reduced for symmetry. 4
1, 1, 0, 4, 42, 9050, 6965359, 26721852461, 429651752290375, 31194475941824888769 (list; graph; refs; listen; history; text; internal format)



The sequence counts the distinct closed paths that visit every cell of an n-by-n square lattice at least once, that never cross any edge between adjacent squares more than once, and that do not self-intersect. Paths related by rotation and/or reflection of the square lattice are not considered distinct.

Are a(1) and a(2) the only two terms equal to 1? And is a(3) the only term equal to 0? - Daniel Forgues, Nov 24 2011

The answer is yes: There are several patterns that can straightforwardly be generalized to any grid of any size n>3, like e.g., #13 and #6347 of the graphics for a(6) (resp. #24 or #28 of a(5) for odd n). - M. F. Hasler, Nov 24 2011


Table of n, a(n) for n=1..10.

Dale Gerdemann, Video illustration for a(5) = 42

OEIS Wiki, Number of meanders filling out an n-by-n grid (reduced for symmetry)

Jon Wild, Illustration for a(4) = 4

Jon Wild, Illustration for a(5) = 42

Jon Wild, Illustration for a(6) = 9050 [Warning: this is a large file!]


a(1) counts the paths that visit the single cell of the 1-by-1 lattice: there is one, the "fat dot".

The 4 solutions for n=4, 42 solutions for n=5 and 9050 solutions for n=6 are illustrated in the supporting png files.


Cf. A200749 (version not reduced for symmetry).

Cf. A200893 (meanders on n-by-k rectangles instead of squares, reduced for symmetry)

Cf. A201145 (meanders on n-by-k rectangles, not reduced for symmetry)

Sequence in context: A134356 A156479 A111829 * A198209 A220774 A186678

Adjacent sequences:  A199997 A199998 A199999 * A200001 A200002 A200003




Jon Wild, Nov 20 2011


a(8) and a(10) from Alex Chernov, May 28 2012

a(9) from Alex Chernov, added by Max Alekseyev, Jul 21 2013



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Last modified April 20 16:29 EDT 2014. Contains 240807 sequences.