Ken's Puzzle of the Week

Lacing (Short) Shoes

In how many ways can you lace shoes with 2/3/4 pairs of eyelets?  Label the eyelet pairs from top to bottom:   
 A B
 C D
(E F)
(G H)


Feel free to extend this to more pairs.  However, I've read of mathematicians analyzing this problem for seven pairs of eyelets and finding millions of solutions.  Is there a formula or recursive approach to this?

Source: I didn't find the original source (if you find it, let me know.)  Here are some related links: Optimum Shoe Lacing, Ian's Shoelace Site.
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