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A349320 a(n) is the Y-coordinate of the n-th point of the hexdragon curve; sequence A349319 gives X-coordinates.

%I A349320 #17 Oct 11 2022 00:57:52
%S A349320 0,0,1,2,3,3,4,5,5,4,4,5,6,6,7,8,9,9,10,11,11,10,10,11,11,10,9,9,8,7,
%T A349320 7,8,8,7,7,8,9,9,10,11,12,12,13,14,14,13,13,14,15,15,16,17,18,18,19,
%U A349320 20,20,19,19,20,20,19,18,18,17,16,16,17,17,16,16,17,17
%N A349320 a(n) is the Y-coordinate of the n-th point of the hexdragon curve; sequence A349319 gives X-coordinates.
%C A349320 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 A349320            Y
%C A349320           /
%C A349320          /
%C A349320         0 ---- X
%C A349320 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 A349320 Rémy Sigrist, <a href="/A349320/b349320.txt">Table of n, a(n) for n = 0..4373</a>
%H A349320 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.31.4 Terdragon and hexdragon.
%H A349320 Rémy Sigrist, <a href="/A349319/a349319.png">Representation of the hexdragon curve after 6 iterations</a>
%H A349320 Rémy Sigrist, <a href="/A349320/a349320.gp.txt">PARI program for A349320</a>
%H A349320 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%e A349320 The hexdragon curve starts as follows:
%e A349320               16-17
%e A349320               /
%e A349320             15
%e A349320               \
%e A349320               14
%e A349320               /
%e A349320          12-13
%e A349320          /
%e A349320        11      8--7
%e A349320          \    /    \
%e A349320          10--9      6
%e A349320                    /
%e A349320                4--5
%e A349320               /
%e A349320              3
%e A349320               \
%e A349320                2
%e A349320               /
%e A349320           0--1
%e A349320 - so a(0) = a(1) = 0,
%e A349320      a(2) = 1,
%e A349320      a(3) = 2,
%e A349320      a(4) = a(5) = 3,
%e A349320      a(6) = a(9) = a(10) = 4,
%e A349320      a(7) = a(8) = a(11) = 5,
%e A349320      a(12) = a(13) = 6,
%e A349320      a(14) = 7,
%e A349320      a(15) = 8,
%e A349320      a(16) = a(17) = 9.
%o A349320 (PARI) See Links section.
%Y A349320 See A349041 for a similar sequence.
%Y A349320 Cf. A349319.
%K A349320 sign
%O A349320 0,4
%A A349320 _Rémy Sigrist_, Nov 14 2021