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
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.
AUTHOR
Antti Karttunen, Jul 29 2009
EXTENSIONS
Links to further derived sequences added by Antti Karttunen, Sep 21 2009
STATUS
approved