How to lace a shoe

[all at abouthugo.de]

Neil, SeqFans,

(see A078601, A078602, A078629)
I made some experiments using real hardware. Since the arrangement of
the
laces in the "crossing section" really makes a difference in the
mechanical/
friction behavior, there seems to be another sequence that takes into
account the different arrangement of the laces when they cross each
other.
I have taken some pictures:
http://www.randomwalk.de/shoelace/l2_1.jpg
http://www.randomwalk.de/shoelace/l2_2.jpg
http://www.randomwalk.de/shoelace/l2_3.jpg
http://www.randomwalk.de/shoelace/l2_4.jpg
http://www.randomwalk.de/shoelace/l2_5.jpg

4 and 5 are obviously different. Another condition is that the laces
enter the "free end" eylets 1 and 2n from the outer side of the shoe.
The corresponding sequence would start 1, 5, did not finish counting
a(3)
with my hardware setup ;-)
The following terms will have interesting complexity, e.g. two examples
from a(4)
http://www.randomwalk.de/shoelace/l4a.jpg
http://www.randomwalk.de/shoelace/l4b.jpg

Happy counting
Hugo Pfoertner
http://www.pfoertner.org/