

A200893


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


4



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
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OFFSET

1,10


COMMENTS

The sequence counts the distinct closed paths that visit every cell of an nbyk rectangular 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 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



