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%I #19 Feb 10 2019 01:56:25
%S 1,3,7,10,63,157,456,1830,0,8538,23114,61804,165123,0,2339000
%N Number of shapes of grid-filling curves of order 6*n+1 (on the tri-hexagonal grid) with turns by +-60 and +-120 degrees that are generated by Lindenmayer-systems with just one symbol apart from the turns.
%C Such curves exist only for n such that 6*n+1 is a term of A003136, these values 6*n+1 are given in A260682.
%C The first such curve, the only one of order 7, was discovered by Jeffrey Ventrella, see page 105 in the Ventrella reference.
%H Joerg Arndt, <a href="https://arxiv.org/abs/1607.02433">Plane-filling curves on all uniform grids</a>, arXiv preprint arXiv:1607.02433 [math.CO], 2016.
%H Jeffrey J. Ventrella, <a href="http://archive.org/download/BrainfillingCurves-AFractalBestiary/">Brain-Filling Curves: A Fractal Bestiary</a>, LuLu.com, (2012).
%Y Cf. A234434 (shapes on the triangular grid), A265685 (shapes on the square grid).
%K nonn,hard,more
%O 1,2
%A _Joerg Arndt_, Dec 13 2015
%E a(11) - a(15) from _Joerg Arndt_, Feb 10 2019
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