cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Dec 11 2002

Keywords

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

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

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.

Original entry on oeis.org

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

Views

Author

Hugo Pfoertner, Dec 18 2002

Keywords

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

Crossrefs

Cf. A078698, A078700, A078675.

Formula

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

Extensions

More terms from Hugo Pfoertner, Mar 11 2025

A078676 Number of symmetric ways to lace a shoe that has n pairs of eyelets.

Original entry on oeis.org

1, 2, 7, 43, 350, 3547, 43011, 607042
Offset: 1

Views

Author

N. J. A. Sloane, Dec 11 2002

Keywords

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.

Examples

			a(3) = 7: 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 symmetric lacings are: 124356 154326 153426 142536 145236 132546 135246.

Links

Crossrefs

Cf. A078602 for directed solutions, A078675 for undirected solutions.

Extensions

a(7) and a(8) from Hugo Pfoertner, Jan 22 2005
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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