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A349041 a(n) is the Y-coordinate of the n-th point of the terdragon curve; sequence A349040 gives X-coordinates.

%I A349041 #15 Nov 14 2021 10:05:21
%S A349041 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 A349041 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 A349041 6,5,6,5,6,6,7,7,8,7,8,8,9,9,10,9,10,9
%N A349041 a(n) is the Y-coordinate of the n-th point of the terdragon curve; sequence A349040 gives X-coordinates.
%C A349041 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 A349041            Y
%C A349041           /
%C A349041          /
%C A349041         0 ---- X
%C A349041 The terdragon curve can be represented using an L-system.
%C A349041 A265671, when interpreted as a sequence of directions, yields the same curve.
%H A349041 Rémy Sigrist, <a href="/A349041/b349041.txt">Table of n, a(n) for n = 0..6561</a>
%H A349041 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 A349041 Rémy Sigrist, <a href="/A349041/a349041.gp.txt">PARI program for A349041</a>
%H A349041 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dragon_curve#Terdragon">Terdragon</a>
%H A349041 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%e A349041 The terdragon curve starts (on a hexagonal lattice) as follows:
%e A349041               +-----+
%e A349041               8\    9
%e A349041                 \
%e A349041            +-----+7
%e A349041            6\   /4\
%e A349041              \5/   \
%e A349041               +-----+
%e A349041               2\   3
%e A349041                 \
%e A349041            +-----+
%e A349041            0     1
%e A349041 - so a(0) = a(1) = 0,
%e A349041      a(2) = a(3) = a(5) = 1,
%e A349041      a(4) = a(6) = a(7) = 2,
%e A349041      a(8) = a(9) = 3.
%o A349041 (PARI) See Links section.
%Y A349041 Cf. A080846, A265671, A349040.
%K A349041 sign
%O A349041 0,5
%A A349041 _Rémy Sigrist_, Nov 06 2021