A200749 Number of meanders filling out an n X n grid, not reduced for symmetry.

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

Offset: 1

Author

Jon Wild, Nov 21 2011

Keywords

• nonn

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

Examples

			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.
		

Links

• Jon Wild, Illustration for a(4) = 11.

Crossrefs

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

Extensions

a(8) - a(15) from Alex Chernov, Jan 01 2012

a(16) - a(17) from Zhao Hui Du, Apr 01 2014