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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)



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.


Table of n, a(n) for n=1..8.

N. J. A. Sloane, FORTRAN program [Uses nexper from Nijenhuis and Wilf, Combinatorial Algorithms, 1st. ed.. Compile with f90.]

Index entries for sequences related to shoe lacings


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.


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

Adjacent sequences:  A078599 A078600 A078601 * A078603 A078604 A078605




N. J. A. Sloane, Dec 11 2002


a(7) and a(8) from Hugo Pfoertner, Jan 22 2005



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Last modified April 23 05:42 EDT 2021. Contains 343199 sequences. (Running on oeis4.)