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A163359 Hilbert curve in N x N grid, starting downwards from the top-left corner, listed by descending antidiagonals.

%I A163359 #22 Feb 16 2025 08:33:11
%S A163359 0,3,1,4,2,14,5,7,13,15,58,6,8,12,16,59,57,9,11,17,19,60,56,54,10,30,
%T A163359 18,20,63,61,55,53,31,29,23,21,64,62,50,52,32,28,24,22,234,65,67,49,
%U A163359 51,33,35,27,25,233,235,78,66,68,48,46,34,36,26,230,232,236,79,77,71
%N A163359 Hilbert curve in N x N grid, starting downwards from the top-left corner, listed by descending antidiagonals.
%H A163359 A. Karttunen, <a href="/A163359/b163359.txt">Table of n, a(n) for n = 0..32895</a>
%H A163359 David Hilbert, <a href="https://doi.org/10.1007/BF01199431">Ueber die stetige Abbildung einer Linie auf ein Flächenstück</a>, Mathematische Annalen, volume 38, number 3, 1891, pages 459-460.  Also <a href="https://eudml.org/doc/157555">EUDML</a> (link to GDZ).
%H A163359 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HilbertCurve.html">Hilbert curve</a>
%H A163359 Wikipedia, <a href="http://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>
%H A163359 Wikipedia, <a href="http://en.wikipedia.org/wiki/Space-filling_curve">Space-filling curve</a>
%H A163359 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%e A163359 The top left 8x8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
%e A163359    +0 +3 +4 +5 58 59 60 63
%e A163359    +1 +2 +7 +6 57 56 61 62
%e A163359    14 13 +8 +9 54 55 50 49
%e A163359    15 12 11 10 53 52 51 48
%e A163359    16 17 30 31 32 33 46 47
%e A163359    19 18 29 28 35 34 45 44
%e A163359    20 23 24 27 36 39 40 43
%e A163359    21 22 25 26 37 38 41 42
%t A163359 b[{n_, k_}, {m_}] := (A[n, k] = m-1);
%t A163359 MapIndexed[b, List @@ HilbertCurve[4][[1]]];
%t A163359 Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Mar 07 2021 *)
%Y A163359 Transpose: A163357, a(n) = A163357(A061579(n)). Inverse: A163360. One-based version: A163363. Row sums: A163365. Row 0: A163483. Column 0: A163482. Central diagonal: A062880.
%Y A163359 See also A163334 and A163336 for the Peano curve.
%K A163359 nonn,tabl
%O A163359 0,2
%A A163359 _Antti Karttunen_, Jul 29 2009