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

0,3

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

Formula

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

Example

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

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 *)

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.

Sequence in context: A157323 A016549 A147584 * A179087 A217013 A058991

Adjacent sequences: A163354 A163355 A163356 * A163358 A163359 A163360

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