A268950 Number of perfectly looping walks containing n pieces from the set described in the links.

0, 0, 0, 2, 1, 5, 7, 33, 74, 304, 986

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], doi:10.1515/rmm-2016-0006.

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