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