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A078698
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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.
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5
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OFFSET
| 1,2
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COMMENTS
| 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,
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REFERENCES
| C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 494.
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LINKS
| Hugo Pfoertner, FORTRAN program and results for N=2,3,4
Index entries for sequences related to shoe lacings
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FORMULA
| Conjecture: a(n) = (n-1)!^2*A051286(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 14 2005
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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.
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PROG
| FORTRAN program provided at Pfoertner link
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CROSSREFS
| Cf. A078700, A078702, A078602.
Sequence in context: A084948 A187661 A009236 * A090728 A185281 A090309
Adjacent sequences: A078695 A078696 A078697 * A078699 A078700 A078701
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Dec 18 2002
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