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A268950 Number of perfectly looping walks containing n pieces from the set described in the links. 0
0, 0, 0, 2, 1, 5, 7, 33, 74, 304, 986 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

These perfectly looping walks are similar, but still different from self-avoiding polygons on the square lattice (A002931) and allow one to realize toy tracks.

Rotations, reflections and translations are allowed.

LINKS

Table of n, a(n) for n=1..11.

Jérôme Bastien, Détails du Brevet (Patent for a Circuit suitable for guiding a miniature vehicle), 2012, in French.

Jérôme Bastien, Catalogue de plans pour le système Easyloop (a complete set of examples available).

Jérôme Bastien, Construction and enumeration of circuits capable of guiding a miniature vehicle, Recreational Mathematics Magazine, 3 (2016), 5-42, arXiv:1603.08775 [math.CO].

EXAMPLE

Some examples are given in the linked paper arxiv.org:1603.08775:

* the a(7)=7 tracks are plotted in Figure 14, p. 24

* some of a(8)=33 tracks are plotted in Figure 15, p. 25

* some of a(9)=74 tracks are plotted in Figure 16, p. 26

CROSSREFS

Cf. A002931

Sequence in context: A193662 A279508 A175770 * A141507 A193603 A059274

Adjacent sequences:  A268947 A268948 A268949 * A268951 A268952 A268953

KEYWORD

nonn,more

AUTHOR

Jérôme Bastien, Apr 25 2016

STATUS

approved

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Last modified April 23 14:15 EDT 2019. Contains 322386 sequences. (Running on oeis4.)