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.

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, 438, 0, 0, 1402, 0, 4232, 0, 3202, 2242, 0, 0, 14316, 5080, 0, 0, 0, 11122, 0, 0, 0, 12374, 155305, 0, 152602, 77469

Offset

0,5

Comments

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

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

Links

Table of n, a(n) for n=0..53.

Jörg Arndt, Julia Handl, Plane-filling Folding Curves on the Square Grid, Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture; Stockholm (2018).

Crossrefs

Cf. A296147 (nonzero terms of this sequence).

Sequence in context: A298133 A298070 A298719 * A121178 A175917 A320525

Adjacent sequences: A296145 A296146 A296147 * A296149 A296150 A296151

Keyword

nonn,hard,more

Author

Joerg Arndt and Julia Handl, Dec 06 2017

Status

approved