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

%I A334484 #18 Jun 09 2022 08:47:07
%S A334484 0,0,1,2,3,3,2,1,0,0,1,1,0,0,1,2,2,3,4,5,5,4,4,5,6,6,7,8,9,9,8,8,9,10,
%T A334484 10,11,12,12,13,14,15,15,14,13,12,12,11,10,10,9,8,8,9,9,8,7,6,6,5,4,4,
%U A334484 5,5,4,3,2,2,1,0,0,1,1,0,0,1,2,3,3,2,1,0,0
%N A334484 a(n) is the Y-coordinate of the n-th point of the Sierpinski arrowhead curve; sequence A334483 gives X-coordinates.
%C A334484 Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
%C A334484            Y
%C A334484           /
%C A334484          /
%C A334484         0 ---- X
%H A334484 Rémy Sigrist, <a href="/A334484/b334484.txt">Table of n, a(n) for n = 0..2187</a>
%H A334484 Rémy Sigrist, <a href="/A334484/a334484.gp.txt">PARI program for A334484</a>
%H A334484 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_curve#Arrowhead_curve">Arrowhead curve</a>
%H A334484 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A334484 A262174(1 + A334483(n) + a(n), 1 + a(n)) = 1 + n for any n >= 0.
%e A334484 The Sierpinski arrowhead curve starts (on a hexagonal lattice) as follows:
%e A334484                          +
%e A334484                         27\
%e A334484                            \
%e A334484                             +
%e A334484                            /26
%e A334484                           /
%e A334484                     +----+
%e A334484                    /24   25
%e A334484                   /
%e A334484                  +          +----+
%e A334484                 23\        /20  19\
%e A334484                    \      /        \
%e A334484                     +----+          +
%e A334484                     22   21        /18
%e A334484                                   /
%e A334484             +----+               +
%e A334484            /4    5\             17\
%e A334484           /        \               \
%e A334484          +          +               +----+
%e A334484          3\        /6               16  15\
%e A334484            \      /                        \
%e A334484             +    +          +----+          +
%e A334484            /2    7\        /10  11\        /14
%e A334484           /        \      /        \      /
%e A334484     +----+          +----+          +----+
%e A334484     0    1          8    9          12   13
%e A334484 - hence a(3) = a(6) = a(15) = a(16) = 2.
%o A334484 (PARI) See Links section.
%Y A334484 Cf. A262174, A334483.
%K A334484 nonn,look
%O A334484 0,4
%A A334484 _Rémy Sigrist_, May 03 2020