A349219 - OEIS

%I #11 Nov 14 2021 02:59:31

%S 0,0,1,1,0,0,1,1,2,1,2,2,3,2,3,3,4,4,3,3,4,4,3,3,2,3,2,2,1,1,2,2,1,1,

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

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

%N a(n) is the Y-coordinate of the n-th point of the 7-dragon curve; sequence A349218 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 7-dragon curve can be represented using an L-system.

%H Rémy Sigrist, <a href="/A349219/b349219.txt">Table of n, a(n) for n = 0..16807</a>

%H 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 Rémy Sigrist, <a href="/A349219/a349219.gp.txt">PARI program for A349219</a>

%H Jeffrey Ventrella, <a href="http://www.fractalcurves.com/Root7.html">Brainfilling Curves: The Root 7 Family</a>

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

%e The 7-dragon curve starts as follows:

%e          14    12

%e           \   / \

%e            \ /   \

%e           10,13--8,11

%e              \   / \

%e               \ /   \

%e          2---3,6,9---7

%e           \   / \

%e            \ /   \

%e       0----1,4----5

%e - so a(0) = a(1) = a(4) = a(5) = 0,

%e      a(2) = a(3) = a(6) = a(7) = a(9) = 1,

%e      a(8) = a(10) = a(11) = a(13) = 2,

%e      a(12) = a(14) = 3.

%o (PARI) See Links section.

%Y See A349041 and A349198 for similar sequences.

%Y Cf. A349218.

%K sign

%O 0,9

%A _Rémy Sigrist_, Nov 11 2021