A078702 Number of ways to lace a shoe that has n pairs of eyelets such that each eyelet has at least one direct connection to the opposite side.

1, 2, 13, 213, 7584, 454380, 39665160, 4775586480, 756765576000, 152553490810560, 38148245068953600, 11587644586640707200, 4202354709635579481600, 1793612851748170637184000, 889985376998423302704307200, 508018135094443467957310848000, 330553193467656241628008759296000

Offset: 1

Author

Hugo Pfoertner, Dec 18 2002

Keywords

• nonn

Comments

The lace is "undirected": reversing the order of eyelets along the path does not count as a different solution. It must begin and end at the extreme pair of eyelets,

Examples

			a(3) = 13: 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 135246 125346 124536 125436 152346 153246 152436 154236.
		

Links

• Index entries for sequences related to shoe lacings

Crossrefs

Cf. A078698, A078700, A078675.

Formula

a(n) = (A078698(n) + A078700(n))/2.

Extensions

More terms from Hugo Pfoertner, Mar 11 2025