A296147 Number of shapes of grid-filling curves of order A001481(n) (on the square grid) with turns by +-90 degrees that are generated by folding morphisms.

1, 1, 1, 2, 2, 6, 3, 20, 14, 44, 32, 69, 212, 287, 796, 438, 1402, 4232, 3202, 2242, 14316, 5080, 11122, 12374, 155305, 152602, 77469

Offset

1,4

Comments

a(1) and a(2) correspond to the trivial (empty and single-stroke) curves of orders 0 and 1 respectively.

Links

Table of n, a(n) for n=1..27.

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. A296148 (same sequence, including zero terms).

Cf. A265685 (simple curves of order 4*n+1).

Sequence in context: A304987 A305814 A266479 * A130712 A276075 A321908

Adjacent sequences: A296144 A296145 A296146 * A296148 A296149 A296150

Keyword

nonn,hard,more

Author

Joerg Arndt and Julia Handl, Dec 06 2017

Status

approved