A078602 Number of ways to lace a shoe that has n pairs of eyelets.

1, 2, 21, 601, 34278, 3144357, 421928841, 77832868334

Offset: 1

Author

N. J. A. Sloane, Dec 11 2002

Keywords

• nonn
• more

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 "directed": reversing the order of eyelets along the path counts as a different solution.

Examples

			a(3) = 21: 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 together with the following lacings and their mirror images: 125346 124536 125436 152346 153246 152436 154236.
		

Links

• N. J. A. Sloane, FORTRAN program [Uses nexper from Nijenhuis and Wilf, Combinatorial Algorithms, 1st. ed.. Compile with f90.]
• Index entries for sequences related to shoe lacings

Crossrefs

Cf. A078675 (undirected solutions), A078676 (symmetric solutions). See A078601 and A078629 for other ways of counting lacings.

Cf. A072503.

Extensions

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