A296148 - OEIS

A296148

Number of shapes of grid-filling curves of order n (on the square grid) with turns by +-90 degrees that are generated by folding morphisms.

%I #10 Oct 18 2019 11:50:25

%S 1,1,1,0,2,2,0,0,6,3,20,0,0,14,0,0,44,32,69,0,212,0,0,0,0,287,796,0,0,

%T 438,0,0,1402,0,4232,0,3202,2242,0,0,14316,5080,0,0,0,11122,0,0,0,

%U 12374,155305,0,152602,77469

%N Number of shapes of grid-filling curves of order n (on the square grid) with turns by +-90 degrees that are generated by folding morphisms.

%C a(0)=1 and a(1)=1 correspond to the trivial (empty and single-stroke) curves of orders 0 and 1 respectively.

%C a(2) = 1 corresponds to the Heighway-Harter dragon (also known as paperfolding dragon).

%H Jörg Arndt, Julia Handl, <a href="http://archive.bridgesmathart.org/2018/bridges2018-179.html">Plane-filling Folding Curves on the Square Grid</a>, Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture; Stockholm (2018).

%Y Cf. A296147 (nonzero terms of this sequence).

%K nonn,hard,more

%O 0,5

%A _Joerg Arndt_ and Julia Handl, Dec 06 2017