

A200749


Number of meanders filling out an n X n grid, not reduced for symmetry.


3



1, 1, 0, 11, 320, 71648, 55717584, 213773992667, 3437213982024260, 249555807519163873078, 78627163663841340597702692, 109477494899001088619906813170744, 666376868834051436218404625691790011056, 17813932068751803215543399261217225231408150272, 2084618062581510894785237376608868017658716989948775752, 1069049587048126292657245511018395164729584995637677006604201633, 2399885835948485973061191866831331382214612321025714609065977840609754872
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OFFSET

1,4


COMMENTS

The sequence counts the 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 counted separately.


LINKS

Table of n, a(n) for n=1..17.
Jon Wild, Illustration for a(4) = 11.


EXAMPLE

a(1) counts the paths that visit the single cell of the 1 X 1 lattice: there is one, the "fat dot".
The 11 solutions for n=4 are illustrated in the supporting .png file.


CROSSREFS

A200000 gives the reduced version of the sequence (rotations/reflections not considered distinct).
Sequence in context: A219979 A115609 A166053 * A324422 A270815 A197448
Adjacent sequences: A200746 A200747 A200748 * A200750 A200751 A200752


KEYWORD

nonn


AUTHOR

Jon Wild, Nov 21 2011


EXTENSIONS

a(8)  a(15) from Alex Chernov, Jan 01 2012
a(16)  a(17) from Zhao Hui Du, Apr 01 2014


STATUS

approved



