

A163334


Hilbert II curve in N X N 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), ...


37



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

0,3


LINKS

A. Karttunen, Table of n, a(n) for n = 0..13202
Eric Weisstein's World of Mathematics, Hilbert curve
Wikipedia, Selfavoiding walk
Wikipedia, Spacefilling 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


FORMULA

a(n) = A163332(A163328(n)).


EXAMPLE

The top left 9 X 9 corner of the array shows how this surjective selfavoiding walk begins (connect the terms in numerical order, 0123...):
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


CROSSREFS

Transpose: A163336. Inverse: A163335. Onebased version: A163338. Row sums: A163342. Row 0: A163480. Column 0: A163481. Central diagonal: A163343. See A163357 & A163359 for other Hilbert curves.
See also: A163528A163529, A163531, A163534, A163536, A163897.
Sequence in context: A334206 A006666 A267830 * A029683 A063567 A072223
Adjacent sequences: A163331 A163332 A163333 * A163335 A163336 A163337


KEYWORD

nonn,tabl,look


AUTHOR

Antti Karttunen, Jul 29 2009


EXTENSIONS

Links to further derived sequences added by Antti Karttunen, Sep 21 2009


STATUS

approved



