

A200000


Number of meanders filling out an n X n grid, reduced for symmetry.


5



1, 1, 0, 4, 42, 9050, 6965359, 26721852461, 429651752290375, 31194475941824888769, 9828395457980805457337560, 13684686862375136981850903785368, 83297108604256429529069019958551956425, 2226741508593975401942934273354241209226704830, 260577257822688861848154672171293101310412373160498171, 133631198381015786582155688877301469836628906260462969996612568, 299985729493560746632648983353916422875677601725131683097521792924081609
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OFFSET

1,4


COMMENTS

The sequence counts the distinct closed paths that visit every cell of an n X n square lattice at least once, that never cross any edge between adjacent squares more than once, and that do not selfintersect. 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, 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


LINKS



EXAMPLE

a(1) counts the paths that visit the single cell of the 1 X 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.


CROSSREFS

Cf. A200749 (version not reduced for symmetry).
Cf. A200893 (meanders on n X k rectangles instead of squares, reduced for symmetry).
Cf. A201145 (meanders on n X k rectangles, not reduced for symmetry).


KEYWORD

nonn,nice


AUTHOR



EXTENSIONS



STATUS

approved



