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A163357
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Hilbert curve in NxN grid, starting rightwards from the top-left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
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34
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0, 1, 3, 14, 2, 4, 15, 13, 7, 5, 16, 12, 8, 6, 58, 19, 17, 11, 9, 57, 59, 20, 18, 30, 10, 54, 56, 60, 21, 23, 29, 31, 53, 55, 61, 63, 234, 22, 24, 28, 32, 52, 50, 62, 64, 235, 233, 25, 27, 35, 33, 51, 49, 67, 65, 236, 232, 230, 26, 36, 34, 46, 48, 68, 66, 78, 239, 237, 231
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Karttunen, Table of n, a(n) for n = 0..32895
Eric Weisstein's World of Mathematics, Hilbert curve
Wikipedia, Self-avoiding walk
Wikipedia, Space-filling curve
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| a(n) = A163355(A054238(n)).
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EXAMPLE
| The top left 8x8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
+0 +1 14 15 16 19 20 21
+3 +2 13 12 17 18 23 22
+4 +7 +8 11 30 29 24 25
+5 +6 +9 10 31 28 27 26
58 57 54 53 32 35 36 37
59 56 55 52 33 34 39 38
60 61 50 51 46 45 40 41
63 62 49 48 47 44 43 42
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CROSSREFS
| Transpose: A163359. Inverse: A163358. One-based version: A163361. Row sums: A163365. Row 0: A163482. Column 0: A163483. Central diagonal: A062880. See also A163334 & A163336 for other Hilbert curves.
See also: A163540, A163542, A163547, A163898-A163900, A163538, A163539, A163904, A163907, A163917.
Sequence in context: A157323 A016549 A147584 * A179087 A058991 A197423
Adjacent sequences: A163354 A163355 A163356 * A163358 A163359 A163360
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KEYWORD
| nonn,tabl
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jul 29 2009. Links to further derived sequences added Sep 21 2009.
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