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A334483 a(n) is the X-coordinate of the n-th point of the Sierpinski arrowhead curve; sequence A334484 gives Y-coordinates.

%I A334483 #23 Jul 04 2021 16:03:00
%S A334483 0,1,1,0,0,1,2,2,3,4,4,5,6,7,7,6,5,4,4,3,2,2,1,0,0,1,1,0,0,1,2,3,3,2,
%T A334483 1,0,0,1,1,0,0,1,2,2,3,4,5,5,4,4,5,6,6,7,8,8,9,10,11,11,10,9,8,8,9,9,
%U A334483 8,8,9,10,10,11,12,13,13,12,12,13,14,14,15
%N A334483 a(n) is the X-coordinate of the n-th point of the Sierpinski arrowhead curve; sequence A334484 gives Y-coordinates.
%C A334483 Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
%C A334483            Y
%C A334483           /
%C A334483          /
%C A334483         0 ---- X
%C A334483 The Sierpinski arrowhead curve can be represented using an L-system.
%H A334483 Rémy Sigrist, <a href="/A334483/b334483.txt">Table of n, a(n) for n = 0..2187</a>
%H A334483 Rémy Sigrist, <a href="/A334483/a334483.png">Colored line plot of the first 3^7+1 points of the Sierpinski arrowhead curve</a> (where the hue is function of the number of steps from the origin)
%H A334483 Rémy Sigrist, <a href="/A334483/a334483.gp.txt">PARI program for A334483</a>
%H A334483 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_curve#Arrowhead_curve">Arrowhead curve</a>
%H A334483 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A334483 A262174(1 + a(n) + A334484(n), 1 + A334484(n)) = 1 + n for any n >= 0.
%e A334483 The Sierpinski arrowhead curve starts (on a hexagonal lattice) as follows:
%e A334483                          +
%e A334483                         27\
%e A334483                            \
%e A334483                             +
%e A334483                            /26
%e A334483                           /
%e A334483                     +----+
%e A334483                    /24   25
%e A334483                   /
%e A334483                  +          +----+
%e A334483                 23\        /20  19\
%e A334483                    \      /        \
%e A334483                     +----+          +
%e A334483                     22   21        /18
%e A334483                                   /
%e A334483             +----+               +
%e A334483            /4    5\             17\
%e A334483           /        \               \
%e A334483          +          +               +----+
%e A334483          3\        /6               16  15\
%e A334483            \      /                        \
%e A334483             +    +          +----+          +
%e A334483            /2    7\        /10  11\        /14
%e A334483           /        \      /        \      /
%e A334483     +----+          +----+          +----+
%e A334483     0    1          8    9          12   13
%e A334483 - hence a(6) = a(7) = a(20) = a(21) = 2.
%o A334483 (PARI) See Links section.
%Y A334483 Cf. A262174, A307672, A334484.
%K A334483 nonn,look
%O A334483 0,7
%A A334483 _Rémy Sigrist_, May 03 2020