

A163357


Hilbert curve in N X N grid, starting rightwards from the topleft corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...


38



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, 56, 60, 21, 23, 29, 31, 53, 55, 61, 63, 234, 22, 24, 28, 32, 52, 50, 62, 64, 235, 233, 25, 27, 35, 33, 51, 49, 67, 65, 236, 232, 230, 26, 36, 34, 46, 48, 68, 66, 78, 239, 237, 231
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OFFSET

0,3


LINKS

A. Karttunen, Table of n, a(n) for n = 0..32895
Eric Weisstein's World of Mathematics, Hilbert curve
Wikipedia, Selfavoiding walk
Wikipedia, Spacefilling curve
Index entries for sequences that are permutations of the natural numbers


FORMULA

a(n) = A163355(A054238(n)).


EXAMPLE

The top left 8 X 8 corner of the array shows how this surjective selfavoiding walk begins (connect the terms in numerical order, 0123...):
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


CROSSREFS

Transpose: A163359. Inverse: A163358. Onebased version: A163361. Row sums: A163365. Row 0: A163482. Column 0: A163483. Central diagonal: A062880. See also A163334 & A163336 for other Hilbert curves.
See also: A163540, A163542, A163547, A163898A163900, A163538, A163539, A163904, A163907, A163917.
Sequence in context: A157323 A016549 A147584 * A179087 A217013 A058991
Adjacent sequences: A163354 A163355 A163356 * A163358 A163359 A163360


KEYWORD

nonn,tabl,look


AUTHOR

Antti Karttunen, Jul 29 2009. Links to further derived sequences added Sep 21 2009.


STATUS

approved



