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A078602 Number of ways to lace a shoe that has n pairs of eyelets. 9
1, 2, 21, 601, 34278, 3144357, 421928841, 77832868334 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
LINKS
N. J. A. Sloane, FORTRAN program [Uses nexper from Nijenhuis and Wilf, Combinatorial Algorithms, 1st. ed.. Compile with f90.]
EXAMPLE
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.
CROSSREFS
Cf. A078675 (undirected solutions), A078676 (symmetric solutions). See A078601 and A078629 for other ways of counting lacings.
Sequence in context: A195736 A320653 A302686 * A060319 A095224 A034984
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Dec 11 2002
EXTENSIONS
a(7) and a(8) from Hugo Pfoertner, Jan 22 2005
STATUS
approved

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Last modified February 21 02:59 EST 2024. Contains 370219 sequences. (Running on oeis4.)