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

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn
• tabl

Examples

			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 [phone]
   +1 +2 +7 [phone]
   14 13 +8 [phone]
   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
		

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

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.

Programs

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 *)