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A340328
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a(n) is the Y-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340327 gives X-coordinates.
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3
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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
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0,9
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COMMENTS
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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):
.-.
^ |
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.------>. .------>.
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.
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LINKS
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EXAMPLE
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The curve starts as follows:
+
|42
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+----+
|40 41
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+----+----+
|34 |35 |38
| |39 |
+----+ +----+
|32 33 36 37
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+----+----+ +----+
|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.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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