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%I #15 Oct 10 2022 07:56:32
%S 0,1,1,0,0,1,1,0,-1,-1,-2,-3,-3,-2,-2,-3,-3,-2,-2,-3,-4,-4,-5,-6,-7,
%T -7,-6,-5,-4,-4,-5,-6,-7,-7,-8,-9,-9,-8,-8,-9,-9,-8,-8,-9,-10,-10,-11,
%U -12,-12,-11,-11,-12,-12,-11,-11,-12,-13,-13,-14,-15,-16,-16
%N a(n) is the X-coordinate of the n-th point of the hexdragon curve; sequence A349320 gives Y-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 hexdragon curve can be represented using an L-system obtained from that of the terdragon curve by replacing each "move forward and turn +-120 degrees" step by two "move forward and turn +- 60 degrees" steps.
%H Rémy Sigrist, <a href="/A349319/b349319.txt">Table of n, a(n) for n = 0..4373</a>
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.31.4 Terdragon and hexdragon.
%H Rémy Sigrist, <a href="/A349319/a349319.png">Representation of the hexdragon curve after 6 iterations</a>
%H Rémy Sigrist, <a href="/A349319/a349319.gp.txt">PARI program for A349319</a>
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%e The hexdragon curve starts as follows:
%e 16-17
%e /
%e 15
%e \
%e 14
%e /
%e 12-13
%e /
%e 11 8--7
%e \ / \
%e 10--9 6
%e /
%e 4--5
%e /
%e 3
%e \
%e 2
%e /
%e 0--1
%e - so a(0) = a(3) = a(4) = a(7) = 0,
%e a(1) = a(2) = a(5) = a(6) = 1,
%e a(8) = a(9) = -1,
%e a(10) = a(13) = a(14) = a(17) = -2,
%e a(11) = a(12) = a(15) = a(16) = -3.
%o (PARI) See Links section.
%Y See A349040 for a similar sequence.
%Y Cf. A349320.
%K sign
%O 0,11
%A _Rémy Sigrist_, Nov 14 2021
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