A163359 Hilbert curve in N x N grid, starting downwards from the top-left corner, listed by descending antidiagonals.

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

Offset

0,2

Links

A. Karttunen, Table of n, a(n) for n = 0..32895

David Hilbert, Ueber die stetige Abbildung einer Linie auf ein Flächenstück, Mathematische Annalen, volume 38, number 3, 1891, pages 459-460.  Also EUDML (link to GDZ).

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 nonnegative integers

Example

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

Mathematica

b[{n_, k_}, {m_}] := (A[n, k] = m-1);
MapIndexed[b, List @@ HilbertCurve[4][[1]]];
Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)

Crossrefs

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 and A163336 for the Peano curve.

Sequence in context: A240058 A275896 A340754 * A065256 A016573 A191818

Adjacent sequences: A163356 A163357 A163358 * A163360 A163361 A163362

Keyword

nonn,tabl

Author

Antti Karttunen, Jul 29 2009

Status

approved