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A340321 a(n) is the Y-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340320 gives X-coordinates.

%I A340321 #11 Jan 07 2021 10:31:24
%S A340321 0,0,1,1,0,0,1,1,2,2,3,3,4,4,3,3,2,2,1,1,0,0,1,1,0,0,1,1,2,2,3,3,4,4,
%T A340321 3,3,4,4,5,5,6,6,5,5,6,6,7,7,8,8,9,9,10,10,9,9,10,10,11,11,12,12,13,
%U A340321 13,12,12,11,11,10,10,9,9,10,10,9,9,8,8,7,7,6
%N A340321 a(n) is the Y-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340320 gives X-coordinates.
%C A340321 The curve is built by successively applying the following substitution to an initial vector (1, 0) (the two vertical copies are horizontally flipped):
%C A340321                                *
%C A340321                            .------>.
%C A340321                            ^       |
%C A340321                            |*     *|
%C A340321                        *   |       v   *
%C A340321                    .------>.       .------>.
%C A340321 The quadratic Koch curve is built without horizontal flip.
%H A340321 Rémy Sigrist, <a href="/A340321/b340321.txt">Table of n, a(n) for n = 0..3125</a>
%H A340321 Robert Ferréol (MathCurve), <a href="https://www.mathcurve.com/fractals/kochquadratique/kochquadratique.shtml">Courbe de Koch quadratique</a> [in French]
%H A340321 Rémy Sigrist, <a href="/A340321/a340321.gp.txt">PARI program for A340321</a>
%H A340321 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A340321 a(5^k-m) = a(m) for any k >= 0 and m = 0..5^k.
%e A340321 The curve starts as follows:
%e A340321                      +---+
%e A340321                      |12 |13
%e A340321                      |   |
%e A340321                  +---+   +---+
%e A340321                  |10  11  14 |15
%e A340321                  |           |
%e A340321                  +---+   +---+
%e A340321                   9  |8  |17  16
%e A340321                      |   |
%e A340321          +---+   +---+   +---+   +---+
%e A340321          |2  |3  |6   7   18 |19 |22 |23
%e A340321          |   |   |           |   |   |
%e A340321      +---+   +---+           +---+   +---+
%e A340321       0   1   4   5           20  21  24  25
%e A340321 - so a(0) = a(1) = a(4) = a(5) = a(20) = a(21) = a(24) = a(25) = 0,
%e A340321      a(8) = a(9) = a(16) = a(17) = 2.
%o A340321 (PARI) See Links section.
%Y A340321 See A332250 and A340328 for similar sequences.
%Y A340321 Cf. A340320 (X-coordinates).
%K A340321 nonn
%O A340321 0,9
%A A340321 _Rémy Sigrist_, Jan 04 2021