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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.
3
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, 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, 13, 12, 12, 11, 11, 10, 10, 9, 9, 10, 10, 9, 9, 8, 8, 7, 7, 6
OFFSET
0,9
COMMENTS
The curve is built by successively applying the following substitution to an initial vector (1, 0) (the two vertical copies are horizontally flipped):
*
.------>.
^ |
|* *|
* | v *
.------>. .------>.
The quadratic Koch curve is built without horizontal flip.
FORMULA
a(5^k-m) = a(m) for any k >= 0 and m = 0..5^k.
EXAMPLE
The curve starts as follows:
+---+
|12 |13
| |
+---+ +---+
|10 11 14 |15
| |
+---+ +---+
9 |8 |17 16
| |
+---+ +---+ +---+ +---+
|2 |3 |6 7 18 |19 |22 |23
| | | | | |
+---+ +---+ +---+ +---+
0 1 4 5 20 21 24 25
- so a(0) = a(1) = a(4) = a(5) = a(20) = a(21) = a(24) = a(25) = 0,
a(8) = a(9) = a(16) = a(17) = 2.
PROG
(PARI) See Links section.
CROSSREFS
See A332250 and A340328 for similar sequences.
Cf. A340320 (X-coordinates).
Sequence in context: A252489 A357839 A332250 * A340320 A059998 A361384
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 04 2021
STATUS
approved