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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

%I

%S 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,

%T 52,54,19,23,11,43,39,51,55,59,20,22,24,42,40,38,56,58,60,141,21,25,

%U 29,41,37,69,57,61,425,142,140,26,28,30,36,70,68,62,424,426,143,139

%N 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), ... .

%H Antti Karttunen, <a href="/A163334/b163334.txt">Table of n, a(n) for n = 0..13202</a>

%H E. H. Moore, <a href="https://doi.org/10.1090/S0002-9947-1900-1500526-4">On Certain Crinkly Curves</a>, Transactions of the American Mathematical Society, volume 1, number 1, 1900, pages 72-90. (And <a href="https://doi.org/10.1090/S0002-9947-1900-1500428-3/">errata</a>.) See section 7 (and in figure 3 rotate -90 degrees for the table here).

%H Giuseppe Peano, <a href="https://doi.org/10.1007/BF01199438">Sur une courbe, qui remplit toute une aire plane</a>, Mathematische Annalen, volume 36, number 1, 1890, pages 157-160. Also <a href="https://eudml.org/doc/157489">EUDML</a> (link to GDZ).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HilbertCurve.html">Hilbert curve</a> (this curve called "Hilbert II").

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Space-filling_curve">Space-filling curve</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A163332(A163328(n)).

%e 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-...):

%e 0 1 2 15 16 17 18 19 20

%e 5 4 3 14 13 12 23 22 21

%e 6 7 8 9 10 11 24 25 26

%e 47 46 45 44 43 42 29 28 27

%e 48 49 50 39 40 41 30 31 32

%e 53 52 51 38 37 36 35 34 33

%e 54 55 56 69 70 71 72 73 74

%e 59 58 57 68 67 66 77 76 75

%e 60 61 62 63 64 65 78 79 80

%t b[{n_, k_}, {m_}] := (A[k, n] = m - 1);

%t MapIndexed[b, List @@ PeanoCurve[4][[1]]];

%t Table[A[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Mar 07 2021 *)

%Y Transpose: A163336. Inverse: A163335. One-based version: A163338. Row sums: A163342. Row 0: A163480. Column 0: A163481. Central diagonal: A163343.

%Y See A163357 and A163359 for the Hilbert curve.

%K nonn,tabl,look

%O 0,3

%A _Antti Karttunen_, Jul 29 2009

%E Links to further derived sequences added by _Antti Karttunen_, Sep 21 2009

%E Name corrected by _Kevin Ryde_, Aug 22 2020

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)