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%I #25 Feb 12 2019 02:18:35
%S 1,1,4,6,0,33,39,0,164,335,0,603,2467,0,10412,19692,0,79494,0,155155,
%T 1271455,1272243,0
%N Number of shapes of grid-filling curves of order 4*n+1 (on the square grid) with turns by +-90 degrees that are generated by Lindenmayer-systems with just one symbol apart from the turns.
%C Such curves exist only for n such that 4*n+1 is a term of A057653.
%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 Jörg Arndt, Julia Handl, <a href="http://archive.bridgesmathart.org/2018/bridges2018-179.html">Plane-filling Folding Curves on the Square Grid</a>, 2018. (This paper is about a different class of curves where the Lindenmayer-systems have two no-constant symbols)
%Y Cf. A234434 (shapes on the triangular grid), A265686 (tri-hexagonal grid).
%Y Cf. A296148 (folding curves of order n) and A296149 (folding curves of order 4*n+1).
%Y Cf. A306358 (curve orders with at least two decomposition x^2 + y^2).
%K nonn,hard,more
%O 1,3
%A _Joerg Arndt_, Dec 13 2015
%E a(15)..a(23) from _Joerg Arndt_, Feb 12 2019
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