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

1,3

Comments

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

Links

Table of n, a(n) for n=1..23.

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).

Sequence in context: A316386 A288422 A268437 * A111828 A013249 A013253

Adjacent sequences: A265682 A265683 A265684 * A265686 A265687 A265688

Keyword

nonn,hard,more

Author

Joerg Arndt, Dec 13 2015

Extensions

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

Status

approved