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Search: id:A163336
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| A163336 |
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Hilbert II curve in NxN 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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+0
24
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| 0, 5, 1, 6, 4, 2, 47, 7, 3, 15, 48, 46, 8, 14, 16, 53, 49, 45, 9, 13, 17, 54, 52, 50, 44, 10, 12, 18, 59, 55, 51, 39, 43, 11, 23, 19, 60, 58, 56, 38, 40, 42, 24, 22, 20, 425, 61, 57, 69, 37, 41, 29, 25, 21, 141, 426, 424, 62, 68, 70, 36, 30, 28, 26, 140, 142, 431, 427
(list; table; graph; listen)
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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..3320
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, although this is not the one Peano himself gave).
Index entries for sequences that are permutations of the natural numbers
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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 +5 +6 47 48 53 54 59 60
+1 +4 +7 46 49 52 55 58 61
+2 +3 +8 45 50 51 56 57 62
15 14 +9 44 39 38 69 68 63
16 13 10 43 40 37 70 67 64
17 12 11 42 41 36 71 66 65
18 23 24 29 30 35 72 77 78
19 22 25 28 31 34 73 76 79
20 21 26 27 32 33 74 75 80
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CROSSREFS
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Transpose: A163334. Inverse: A163337. a(n) = A163332(A163330(n)) = A163327(A163333(A163328(n))) = A163334(A061579(n)). One-based version: A163340. Row sums: A163342. Row 0: A163481. Column 0: A163480. Central diagonal: A163343. See A163357 & A163359 for other Hilbert curves.
Sequence in context: A088401 A077491 A086231 this_sequence A131944 A058651 A164105
Adjacent sequences: A163333 A163334 A163335 this_sequence A163337 A163338 A163339
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jul 29 2009
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