A340328 - OEIS

A340328

a(n) is the Y-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340327 gives X-coordinates.

0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 6, 6, 7, 7, 6, 6, 5, 5, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1

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OFFSET

0,9

COMMENTS

The curve is built by successively applying the following substitution to an initial vector (1, 0) (we have 4 copies and a horizontal unit vector):

.-.

^ |

| |

| v

.------>. .------>.

The curve visits once or twice every lattice point (x, y) such that 0 <= y <= x.

The quadratic Koch curve is built from 5 copies at each step.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..5461

Robert Ferréol (MathCurve), Courbe de Koch quadratique [in French]

Rémy Sigrist, PARI program for A340328

Index entries for sequences related to coordinates of 2D curves

EXAMPLE

The curve starts as follows:

|42

+----+

|40 41

+----+----+

|34 |35 |38

| |39 |

+----+ +----+

|32 33 36 37

+----+----+ +----+

|10 |11 |30 |27 |26

| |31 | | |

+----+ +----+----+----+

|8 9 12 |13 |24 25

| |29 |28

+----+----+ +----+----+----+

|2 |3 |6 |15 |14 |19 |22

| |7 | | |18 |23 |

+----+ +----+ +----+ +----+

0 1 4 5 16 17 20 21

- so a(8) = a(9) = a(12) = a(13) = a(24) = a(25) = a(28) = a(29) = 2,

a(40) = a(41) = 6.

PROG

(PARI) See Links section.

CROSSREFS

See A332250 and A340321 for similar sequences.

Cf. A340327 (X-coordinates).

Sequence in context: A339456 A220517 A369053 * A271076 A087175 A188817

Adjacent sequences: A340325 A340326 A340327 * A340329 A340330 A340331

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jan 04 2021

STATUS

approved