|
Search: id:A078698
|
|
|
| A078698 |
|
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. |
|
+0
6
|
| |
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The lace is "directed": reversing the order of eyelets along the path counts as a different solution. It must begin and end at the extreme pair of eyelets,
|
|
LINKS
|
Hugo Pfoertner, FORTRAN program and results for N=2,3,4
Index entries for sequences related to shoe lacings
|
|
FORMULA
|
Conjecture: a(n) = (n-1)!^2*A051286(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 14 2005
|
|
EXAMPLE
|
a(3) = 20: 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 and
the following and their mirror images: 125346 124536 125436 152346 153246 152436 154236.
Examples for n=2,3,4 can be found following the FORTRAN program at given link.
|
|
PROGRAM
|
FORTRAN program provided at Pfoertner link
|
|
CROSSREFS
|
Cf. A078700, A078702, A078602.
Sequence in context: A060164 A084948 A009236 this_sequence A090728 A090309 A002116
Adjacent sequences: A078695 A078696 A078697 this_sequence A078699 A078700 A078701
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 18 2002
|
|
|
Search completed in 0.002 seconds
|
