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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. 4
1, 1, 4, 6, 0, 33, 39, 0, 164, 335, 0, 603, 2467, 0, 10412, 19692, 0, 79494, 0, 155155, 1271455, 1272243, 0 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 22:26 EDT 2021. Contains 343090 sequences. (Running on oeis4.)