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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
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 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, 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
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).
Sequence in context: A355130 A355124 A111829 * A198209 A220774 A296683
KEYWORD
nonn,nice
AUTHOR
Jon Wild, Nov 20 2011
EXTENSIONS
a(8) and a(10) from Alex Chernov, May 28 2012
a(9) from Alex Chernov, added by Max Alekseyev, Jul 21 2013
a(11) to a(17) from Zhao Hui Du, Apr 03 2014
STATUS
approved