A265686 Number of shapes of grid-filling curves of order 6*n+1 (on the tri-hexagonal grid) with turns by +-60 and +-120 degrees that are generated by Lindenmayer-systems with just one symbol apart from the turns.

1, 3, 7, 10, 63, 157, 456, 1830, 0, 8538, 23114, 61804, 165123, 0, 2339000

Offset

1,2

Comments

Such curves exist only for n such that 6*n+1 is a term of A003136, these values 6*n+1 are given in A260682.

The first such curve, the only one of order 7, was discovered by Jeffrey Ventrella, see page 105 in the Ventrella reference.

Links

Table of n, a(n) for n=1..15.

Joerg Arndt, Plane-filling curves on all uniform grids, arXiv preprint arXiv:1607.02433 [math.CO], 2016.

Jeffrey J. Ventrella, Brain-Filling Curves: A Fractal Bestiary, LuLu.com, (2012).

Crossrefs

Cf. A234434 (shapes on the triangular grid), A265685 (shapes on the square grid).

Sequence in context: A101397 A042229 A042373 * A042775 A229596 A125255

Adjacent sequences: A265683 A265684 A265685 * A265687 A265688 A265689

Keyword

nonn,hard,more

Author

Joerg Arndt, Dec 13 2015

Extensions

a(11) - a(15) from Joerg Arndt, Feb 10 2019

Status

approved