%I #15 Nov 14 2021 10:05:21

%S 0,0,1,1,2,1,2,2,3,3,4,3,4,3,3,2,3,2,3,3,4,4,5,4,5,5,6,6,7,6,7,6,6,5,

%T 6,5,6,5,5,4,4,5,5,4,4,3,4,3,4,3,3,2,3,2,3,3,4,4,5,4,5,5,6,6,7,6,7,6,

%U 6,5,6,5,6,6,7,7,8,7,8,8,9,9,10,9,10,9

%N a(n) is the Y-coordinate of the n-th point of the terdragon curve; sequence A349040 gives X-coordinates.

%C Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows (the Y-axis corresponds to the sixth primitive root of unity):

%C Y

%C /

%C /

%C 0 ---- X

%C The terdragon curve can be represented using an L-system.

%C A265671, when interpreted as a sequence of directions, yields the same curve.

%H Rémy Sigrist, <a href="/A349041/b349041.txt">Table of n, a(n) for n = 0..6561</a>

%H Rémy Sigrist, <a href="/A349040/a349040.png">Colored representation of the first 1 + 3^11 points of the terdragon curve</a> (where the hue is function of the number of steps from the origin)

%H Rémy Sigrist, <a href="/A349041/a349041.gp.txt">PARI program for A349041</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dragon_curve#Terdragon">Terdragon</a>

%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%e The terdragon curve starts (on a hexagonal lattice) as follows:

%e +-----+

%e 8\ 9

%e \

%e +-----+7

%e 6\ /4\

%e \5/ \

%e +-----+

%e 2\ 3

%e \

%e +-----+

%e 0 1

%e - so a(0) = a(1) = 0,

%e a(2) = a(3) = a(5) = 1,

%e a(4) = a(6) = a(7) = 2,

%e a(8) = a(9) = 3.

%o (PARI) See Links section.

%Y Cf. A080846, A265671, A349040.

%K sign

%O 0,5

%A _Rémy Sigrist_, Nov 06 2021