

A163336


Hilbert II 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), ...


25



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
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OFFSET

0,2


LINKS

A. Karttunen, Table of n, a(n) for n = 0..3320
Rémy Sigrist, Colored scatterplot of (x, y) such that 0 <= x, y < 3^6 (where the hue is function of T(x, y))
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, although this is not the one Peano himself gave).
Index entries for sequences that are permutations of the natural numbers


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 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


CROSSREFS

Transpose: A163334. Inverse: A163337. a(n) = A163332(A163330(n)) = A163327(A163333(A163328(n))) = A163334(A061579(n)). Onebased version: A163340. Row sums: A163342. Row 0: A163481. Column 0: A163480. Central diagonal: A163343. See A163357 and A163359 for other Hilbert curves.
Sequence in context: A077491 A086231 A201419 * A173898 A200644 A318265
Adjacent sequences: A163333 A163334 A163335 * A163337 A163338 A163339


KEYWORD

nonn,tabl


AUTHOR

Antti Karttunen, Jul 29 2009


STATUS

approved



