A296147 -id:A296147 - cp's OEIS frontend

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

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Joerg Arndt and Julia Handl, Dec 06 2017

nonn
hard
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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).

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

Cf. A296147 (nonzero terms of this sequence).

cp's OEIS Frontend

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.

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