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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), ... 35
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

EXAMPLE

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

CROSSREFS

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: A257700 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

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Last modified December 12 20:04 EST 2017. Contains 295954 sequences.