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%I #35 Apr 02 2021 16:31:25
%S 0,0,0,2,1,5,7,33,74,304,986
%N Number of perfectly looping walks containing n pieces from the set described in the links.
%C 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.
%C Rotations, reflections and translations are allowed.
%H Jérôme Bastien, <a href="http://utbmjb.chez-alice.fr/recherche/brevet_rail/detail_brevet_rails.html">Détails du Brevet (Patent for a Circuit suitable for guiding a miniature vehicle)</a>, 2012, in French.
%H Jérôme Bastien, <a href="http://utbmjb.chez-alice.fr/recherche/brevet_rail/catalogue_exhaustif_11rails.pdf">Catalogue de plans pour le système Easyloop</a> (a complete set of examples available).
%H Jérôme Bastien, <a href="http://rmm.ludus-opuscula.org/PDF_Files/RMM_Number6_December_2016_high.pdf#page=5">Construction and enumeration of circuits capable of guiding a miniature vehicle</a>, Recreational Mathematics Magazine, 3 (2016), 5-42, <a href="https://arxiv.org/abs/1603.08775">arXiv:1603.08775 [math.CO]</a>, doi:<a href="https://doi.org/10.1515/rmm-2016-0006">10.1515/rmm-2016-0006</a>.
%e Some examples are given in the linked paper arxiv.org:1603.08775:
%e * the a(7)=7 tracks are plotted in Figure 14, p. 24
%e * some of a(8)=33 tracks are plotted in Figure 15, p. 25
%e * some of a(9)=74 tracks are plotted in Figure 16, p. 26
%Y Cf. A002931.
%K nonn,more
%O 1,4
%A _Jérôme Bastien_, Apr 25 2016
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