A200893 Triangle read by rows: number of meanders filling out an n X k grid.

1, 0, 1, 0, 1, 0, 0, 1, 1, 4, 0, 1, 1, 14, 42, 0, 1, 3, 63, 843, 9050, 0, 1, 3, 224, 7506, 342743, 6965359, 0, 1, 8, 1022, 71542, 6971973

Offset

1,10

Comments

The sequence counts the distinct closed paths that visit every cell of an n-by-k rectangular 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.

Links

Table of n, a(n) for n=1..34.

Jon Wild, Illustration for T(5,4) = 14

Jon Wild, Illustration for T(6,4)=63

Jon Wild, Illustration for T(7,4)=224

Formula

T(n,3) appears to be equal to A090597.

Example

The 14 solutions for (n,k)=(5,4), 63 solutions for (n,k)=(6,4) and 224 solutions for (n,k)=(7,4) are illustrated in the supporting png files.

Crossrefs

Cf. A200000 (sequence of entries for square grid).

Sequence in context: A218453 A324563 A186372 * A294583 A283675 A294653

Adjacent sequences: A200890 A200891 A200892 * A200894 A200895 A200896

Keyword

nonn,tabl

Author

Jon Wild, Nov 23 2011

Status

approved