cp's OEIS Frontend

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

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