A078629 Number of ways to lace a shoe that has n pairs of eyelets, assuming the lacing satisfies certain conditions.

1, 6, 100, 4244, 311424, 34883924, 5552752356

Offset

1,2

Comments

The lace must follow a Hamiltonian path through the 2n eyelets and cannot pass in order though three adjacent eyelets that are in a line.

The lace is "directed": reversing the order of eyelets along the path counts as a different solution (cf. A078674).

Links

Table of n, a(n) for n=1..7.

N. J. A. Sloane, FORTRAN program

Index entries for sequences related to shoe lacings

Example

Label the eyelets 1, ..., n from front to back on the left and from n+1, ..., 2n from back to front on the right. For n=2 all 6 lacings are allowed: 1 2 3 4, 2 1 3 4, 3 1 2 4, 1 3 2 4, 2 3 1 4, 3 2 1 4.
a(3) = 100: the first few lacings are: 4 2 1 3 5 6, 2 4 1 3 5 6, 1 4 2 3 5 6, 2 1 4 3 5 6, 1 2 4 3 5 6, 1 3 4 2 5 6, 3 1 4 2 5 6, 4 1 3 2 5 6, 1 4 3 2 5 6, 3 4 1 2 5 6, 4 3 1 2 5 6, 3 4 2 1 5 6, 2 4 3 1 5 6, ...

Crossrefs

See A078601 and A078602 for other ways of counting lacings. Cf. A078674.

Sequence in context: A098721 A291837 A214381 * A012497 A012690 A196693

Adjacent sequences: A078626 A078627 A078628 * A078630 A078631 A078632

Keyword

nonn,more

Author

N. J. A. Sloane, Dec 12 2002

Extensions

a(7) from Hugo Pfoertner, Jan 22 2005

Status

approved