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A340321
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a(n) is the Y-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340320 gives X-coordinates.
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3
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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
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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) (the two vertical copies are horizontally flipped):
*
.------>.
^ |
|* *|
* | v *
.------>. .------>.
The quadratic Koch curve is built without horizontal flip.
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LINKS
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FORMULA
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a(5^k-m) = a(m) for any k >= 0 and m = 0..5^k.
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EXAMPLE
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The curve starts as follows:
+---+
|12 |13
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+---+ +---+
|10 11 14 |15
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+---+ +---+
9 |8 |17 16
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+---+ +---+ +---+ +---+
|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.
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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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