OFFSET
0,4
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, Line plot of the first 5462 points
Rémy Sigrist, PARI program for A340327
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(0) = 0,
a(5) = a(6) = a(9) = a(10) = 3.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 04 2021
STATUS
approved