A265685 Number of shapes of grid-filling curves of order 4*n+1 (on the square grid) with turns by +-90 degrees that are generated by Lindenmayer-systems with just one symbol apart from the turns.

1, 1, 4, 6, 0, 33, 39, 0, 164, 335, 0, 603, 2467, 0, 10412, 19692, 0, 79494, 0, 155155, 1271455, 1272243, 0

Offset: 1

Author

Joerg Arndt, Dec 13 2015

Keywords

• nonn
• hard
• more

Comments

Such curves exist only for n such that 4*n+1 is a term of A057653.

Links

• Joerg Arndt, Plane-filling curves on all uniform grids, arXiv preprint arXiv:1607.02433 [math.CO], 2016.
• Jörg Arndt, Julia Handl, Plane-filling Folding Curves on the Square Grid, 2018. (This paper is about a different class of curves where the Lindenmayer-systems have two no-constant symbols)

Crossrefs

Cf. A234434 (shapes on the triangular grid), A265686 (tri-hexagonal grid).

Cf. A296148 (folding curves of order n) and A296149 (folding curves of order 4*n+1).

Cf. A306358 (curve orders with at least two decomposition x^2 + y^2).

Extensions

a(15)..a(23) from Joerg Arndt, Feb 12 2019