login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A078629 Number of ways to lace a shoe that has n pairs of eyelets, assuming the lacing satisfies certain conditions. 4
1, 6, 100, 4244, 311424, 34883924, 5552752356 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 04:00 EDT 2020. Contains 336421 sequences. (Running on oeis4.)