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A163359
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Hilbert curve in N x N grid, starting downwards 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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22
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0, 3, 1, 4, 2, 14, 5, 7, 13, 15, 58, 6, 8, 12, 16, 59, 57, 9, 11, 17, 19, 60, 56, 54, 10, 30, 18, 20, 63, 61, 55, 53, 31, 29, 23, 21, 64, 62, 50, 52, 32, 28, 24, 22, 234, 65, 67, 49, 51, 33, 35, 27, 25, 233, 235, 78, 66, 68, 48, 46, 34, 36, 26, 230, 232, 236, 79, 77, 71
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OFFSET
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0,2
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LINKS
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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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EXAMPLE
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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 +3 +4 +5 58 59 60 63
+1 +2 +7 +6 57 56 61 62
14 13 +8 +9 54 55 50 49
15 12 11 10 53 52 51 48
16 17 30 31 32 33 46 47
19 18 29 28 35 34 45 44
20 23 24 27 36 39 40 43
21 22 25 26 37 38 41 42
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CROSSREFS
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Transpose: A163357, a(n) = A163357(A061579(n)). Inverse: A163360. One-based version: A163363. Row sums: A163365. Row 0: A163483. Column 0: A163482. Central diagonal: A062880. See also A163334 & A163336 for other Hilbert curves.
Sequence in context: A068028 A240058 A275896 * A065256 A016573 A191818
Adjacent sequences: A163356 A163357 A163358 * A163360 A163361 A163362
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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
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STATUS
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approved
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