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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)