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A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed by descending antidiagonals.

%I A163357 #34 Feb 16 2025 08:33:11
%S A163357 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,
%T A163357 56,60,21,23,29,31,53,55,61,63,234,22,24,28,32,52,50,62,64,235,233,25,
%U A163357 27,35,33,51,49,67,65,236,232,230,26,36,34,46,48,68,66,78,239,237,231
%N A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed by descending antidiagonals.
%H A163357 A. Karttunen, <a href="/A163357/b163357.txt">Table of n, a(n) for n = 0..32895</a>
%H A163357 Jörg Arndt, <a href="https://arxiv.org/abs/1607.02433">Plane-filling curves on all uniform grids</a>, arXiv:1607.02433v1 [math.CO], July 11, 2016.
%H A163357 Herman Haverkort, <a href="http://www.win.tue.nl/~hermanh/doku.php?id=recursive_tilings_and_space-filling_curves">Recursive tilings and space-filling curves</a>
%H A163357 Herman Haverkort, <a href="http://www.win.tue.nl/~hermanh/lib/exe/fetch.php?media=research:sound-of-space-filling-curves.pdf">The Sound of Space-Filling Curves</a>, Proc. Bridges 2017, pp. 399-402.
%H A163357 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HilbertCurve.html">Hilbert curve</a>
%H A163357 Wikipedia, <a href="http://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>
%H A163357 Wikipedia, <a href="http://en.wikipedia.org/wiki/Space-filling_curve">Space-filling curve</a>
%H A163357 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%F A163357 a(n) = A163355(A054238(n)).
%e A163357 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-...):
%e A163357    0  1 14 15 16 19 20 21
%e A163357    3  2 13 12 17 18 23 22
%e A163357    4  7  8 11 30 29 24 25
%e A163357    5  6  9 10 31 28 27 26
%e A163357   58 57 54 53 32 35 36 37
%e A163357   59 56 55 52 33 34 39 38
%e A163357   60 61 50 51 46 45 40 41
%e A163357   63 62 49 48 47 44 43 42
%t A163357 b[{n_, k_}, {m_}] := (A[k, n] = m-1);
%t A163357 MapIndexed[b, List @@ HilbertCurve[4][[1]]];
%t A163357 Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Mar 07 2021 *)
%Y A163357 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.
%Y A163357 See also: A163540, A163542, A163547, A163898, A163899, A163900, A163538, A163539, A163904, A163907, A163917.
%K A163357 nonn,tabl,look
%O A163357 0,3
%A A163357 _Antti Karttunen_, Jul 29 2009
%E A163357 Links to further derived sequences added by _Antti Karttunen_, Sep 21 2009