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 A163334 Peano curve in an n X n grid, starting rightwards from the top left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... . 37
 0, 1, 5, 2, 4, 6, 15, 3, 7, 47, 16, 14, 8, 46, 48, 17, 13, 9, 45, 49, 53, 18, 12, 10, 44, 50, 52, 54, 19, 23, 11, 43, 39, 51, 55, 59, 20, 22, 24, 42, 40, 38, 56, 58, 60, 141, 21, 25, 29, 41, 37, 69, 57, 61, 425, 142, 140, 26, 28, 30, 36, 70, 68, 62, 424, 426, 143, 139 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Antti Karttunen, Table of n, a(n) for n = 0..13202 E. H. Moore, On Certain Crinkly Curves, Transactions of the American Mathematical Society, volume 1, number 1, 1900, pages 72-90.  (And errata.)  See section 7 (and in figure 3 rotate -90 degrees for the table here). Giuseppe Peano, Sur une courbe, qui remplit toute une aire plane, Mathematische Annalen, volume 36, number 1, 1890, pages 157-160.  Also EUDML (link to GDZ). Eric Weisstein's World of Mathematics, Hilbert curve (this curve called "Hilbert II"). Wikipedia, Self-avoiding walk Wikipedia, Space-filling curve FORMULA a(n) = A163332(A163328(n)). EXAMPLE The top left 9 X 9 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):    0  1  2 15 16 17 18 19 20    5  4  3 14 13 12 23 22 21    6  7  8  9 10 11 24 25 26   47 46 45 44 43 42 29 28 27   48 49 50 39 40 41 30 31 32   53 52 51 38 37 36 35 34 33   54 55 56 69 70 71 72 73 74   59 58 57 68 67 66 77 76 75   60 61 62 63 64 65 78 79 80 MATHEMATICA b[{n_, k_}, {m_}] := (A[k, n] = m - 1); MapIndexed[b, List @@ PeanoCurve[4][[1]]]; Table[A[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *) CROSSREFS Transpose: A163336. Inverse: A163335. One-based version: A163338. Row sums: A163342. Row 0: A163480. Column 0: A163481. Central diagonal: A163343. See also: A163528-A163529, A163531, A163534, A163536, A163897. See A163357 and A163359 for the Hilbert curve. Sequence in context: A334206 A006666 A267830 * A029683 A063567 A072223 Adjacent sequences:  A163331 A163332 A163333 * A163335 A163336 A163337 KEYWORD nonn,tabl,look AUTHOR Antti Karttunen, Jul 29 2009 EXTENSIONS Links to further derived sequences added by Antti Karttunen, Sep 21 2009 Name corrected by Kevin Ryde, Aug 22 2020 STATUS approved

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Last modified June 24 04:50 EDT 2021. Contains 345416 sequences. (Running on oeis4.)