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 A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed by descending antidiagonals. 39
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)