A078675 Number of ways to lace a shoe that has n pairs of eyelets.

1, 2, 14, 322, 17314, 1573952, 210985926, 38916737688

Offset

1,2

Comments

The lace must pass through each eyelet exactly once, must begin and end at the extreme pair of eyelets and cannot pass in order though three adjacent eyelets that are in a line.

The lace is "undirected": reversing the order of eyelets along the path does not count as a different solution.

Links

Table of n, a(n) for n=1..8.

Index entries for sequences related to shoe lacings

N. J. A. Sloane, FORTRAN program

Example

a(3) = 14: label the eyelets 1,2,3 from front to back on the left side then 4,5,6 from back to front on the right side. The lacings are: 124356 154326 153426 142536 145236 132546 135246 125346 124536 125436 152346 153246 152436 154236.

Crossrefs

Cf. A078602 for directed solutions, A078676 for symmetric solutions.

a(n) = ( A078602(n) + A078676(n) ) / 2

Sequence in context: A139225 A356610 A277035 * A133130 A165696 A180605

Adjacent sequences: A078672 A078673 A078674 * A078676 A078677 A078678

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 2002

Extensions

a(7) and a(8) from Hugo Pfoertner, Jan 22 2005

Status

approved