%I #23 Apr 01 2018 19:29:50

%S 1,1,0,11,320,71648,55717584,213773992667,3437213982024260,

%T 249555807519163873078,78627163663841340597702692,

%U 109477494899001088619906813170744,666376868834051436218404625691790011056,17813932068751803215543399261217225231408150272,2084618062581510894785237376608868017658716989948775752,1069049587048126292657245511018395164729584995637677006604201633,2399885835948485973061191866831331382214612321025714609065977840609754872

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

%C 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 self-intersect. Paths related by rotation and/or reflection of the square lattice are counted separately.

%H Jon Wild, <a href="/A200749/a200749.png">Illustration for a(4) = 11.</a>

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

%e The 11 solutions for n=4 are illustrated in the supporting .png file.

%Y A200000 gives the reduced version of the sequence (rotations/reflections not considered distinct).

%K nonn

%O 1,4

%A _Jon Wild_, Nov 21 2011

%E a(8) - a(15) from _Alex Chernov_, Jan 01 2012

%E a(16) - a(17) from _Zhao Hui Du_, Apr 01 2014