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A163334
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Hilbert II 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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32
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0, 1, 5, 2, 4, 6, 15, 3, 7, 47, 16, 14, 8, 46, 48, 17, 13, 9, 45, 49, 53, 18, 12, 10, 44, 50, 52, 54, 19, 23, 11, 43, 39, 51, 55, 59, 20, 22, 24, 42, 40, 38, 56, 58, 60, 141, 21, 25, 29, 41, 37, 69, 57, 61, 425, 142, 140, 26, 28, 30, 36, 70, 68, 62, 424, 426, 143, 139
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OFFSET
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0,3
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..13202
Eric Weisstein's World of Mathematics, Hilbert curve
Wikipedia, Self-avoiding walk
Wikipedia, Space-filling curve (Wikipedia gives this curve as an example of a Peano curve. However it seems that this one was invented by Hilbert.)
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = A163332(A163328(n)).
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EXAMPLE
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The top left 9x9 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
+0 +1 +2 15 16 17 18 19 20
+5 +4 +3 14 13 12 23 22 21
+6 +7 +8 +9 10 11 24 25 26
47 46 45 44 43 42 29 28 27
48 49 50 39 40 41 30 31 32
53 52 51 38 37 36 35 34 33
54 55 56 69 70 71 72 73 74
59 58 57 68 67 66 77 76 75
60 61 62 63 64 65 78 79 80
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CROSSREFS
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Transpose: A163336. Inverse: A163335. One-based version: A163338. Row sums: A163342. Row 0: A163480. Column 0: A163481. Central diagonal: A163343. See A163357 & A163359 for other Hilbert curves.
See also: A163528-A163529, A163531, A163534, A163536, A163897.
Sequence in context: A202494 A112597 A006666 * A029683 A063567 A072223
Adjacent sequences: A163331 A163332 A163333 * A163335 A163336 A163337
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen, Jul 29 2009. Links to further derived sequences added Sep 21 2009.
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STATUS
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approved
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