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A349218 a(n) is the X-coordinate of the n-th point of the 7-dragon curve; sequence A349219 gives Y-coordinates.

%I A349218 #10 Nov 14 2021 02:59:36
%S A349218 0,1,0,1,1,2,1,2,1,1,0,1,0,0,-1,0,-1,0,0,1,0,1,1,2,2,1,1,2,2,3,2,3,3,
%T A349218 4,3,4,3,3,2,3,2,2,1,2,1,2,2,3,2,3,2,2,1,2,1,1,0,0,1,1,0,0,1,1,0,0,-1,
%U A349218 0,-1,-1,-2,-1,-2,-1,-1,0,-1,0,-1,-1,-2,-1
%N A349218 a(n) is the X-coordinate of the n-th point of the 7-dragon curve; sequence A349219 gives Y-coordinates.
%C A349218 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 A349218            Y
%C A349218           /
%C A349218          /
%C A349218         0 ---- X
%C A349218 The 7-dragon curve can be represented using an L-system.
%H A349218 Rémy Sigrist, <a href="/A349218/b349218.txt">Table of n, a(n) for n = 0..16807</a>
%H A349218 Rémy Sigrist, <a href="/A349218/a349218.png">Colored representation of the first 1 + 7^7 points of the 7-dragon curve</a> (where the hue is function of the number of steps from the origin)
%H A349218 Rémy Sigrist, <a href="/A349218/a349218.gp.txt">PARI program for A349218</a>
%H A349218 Jeffrey Ventrella, <a href="http://www.fractalcurves.com/Root7.html">Brainfilling Curves: The Root 7 Family</a>
%H A349218 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%e A349218 The 7-dragon curve starts as follows:
%e A349218          14    12
%e A349218           \   / \
%e A349218            \ /   \
%e A349218           10,13--8,11
%e A349218              \   / \
%e A349218               \ /   \
%e A349218          2---3,6,9---7
%e A349218           \   / \
%e A349218            \ /   \
%e A349218       0----1,4----5
%e A349218 - so a(0) = a(2) = a(10) = a(12) = a(13) = 0,
%e A349218      a(1) = a(3) = a(4) = a(6) = a(8) = a(9) = a(11) = 1,
%e A349218      a(5) = a(7) = 2,
%e A349218      a(14) = -1.
%o A349218 (PARI) See Links section.
%Y A349218 See A349040 and A349197 for similar sequences.
%Y A349218 Cf. A349219.
%K A349218 sign
%O A349218 0,6
%A A349218 _Rémy Sigrist_, Nov 11 2021