A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed by descending antidiagonals.

0, 1, 3, 14, 2, 4, 15, 13, 7, 5, 16, 12, 8, 6, 58, 19, 17, 11, 9, 57, 59, 20, 18, 30, 10, 54, 56, 60, 21, 23, 29, 31, 53, 55, 61, 63, 234, 22, 24, 28, 32, 52, 50, 62, 64, 235, 233, 25, 27, 35, 33, 51, 49, 67, 65, 236, 232, 230, 26, 36, 34, 46, 48, 68, 66, 78, 239, 237, 231

Offset: 0

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn
• tabl
• look

Examples

			The top left 8 X 8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
   0  1 14 15 16 19 20 21
   3  2 13 12 17 18 23 22
   4  7  8 11 30 29 24 25
   5  6  9 10 31 28 27 26
  58 57 54 53 32 35 36 37
  59 56 55 52 33 34 39 38
  60 61 50 51 46 45 40 41
  63 62 49 48 47 44 43 42
		

Links

• A. Karttunen, Table of n, a(n) for n = 0..32895
• Jörg Arndt, Plane-filling curves on all uniform grids, arXiv:1607.02433v1 [math.CO], July 11, 2016.
• Herman Haverkort, Recursive tilings and space-filling curves
• Herman Haverkort, The Sound of Space-Filling Curves, Proc. Bridges 2017, pp. 399-402.
• 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: A163359. Inverse: A163358. One-based version: A163361. Row sums: A163365. Row 0: A163482. Column 0: A163483. Central diagonal: A062880. See also A163334 & A163336 for the Peano curve.

See also: A163540, A163542, A163547, A163898, A163899, A163900, A163538, A163539, A163904, A163907, A163917.

Programs

Mathematica

b[{n_, k_}, {m_}] := (A[k, n] = 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 *)

Formula

a(n) = A163355(A054238(n)).

Extensions

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