A171171 Corner sequence (starting each round with the corner (SE): 1,2,3).

1, 2, 3, 4, 1, 2, 3, 2, 3, 4, 3, 4, 1, 4, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 1, 4, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 3, 4, 1, 2, 3, 4, 3, 4, 1, 4, 1, 2, 3, 4, 1, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 1, 4, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 3, 4, 1, 2, 3, 4, 3, 4, 1, 4, 1, 2, 3, 4, 1, 4, 1

Offset

1,2

Comments

See A161411, which is the main entry for this sequence.

See also A171170 for another version.

Links

Table of n, a(n) for n=1..105.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Example

================
.......41.......
.......32.......
================
......4141......
......3..2......
......4..1......
......3232......
================
.....41..41.....
.....3....2.....
................
................
.....4....1.....
.....32..32.....
================
....41414141....
....3..23..2....
....4......1....
....32....32....
....41....41....
....3......2....
....4..14..1....
....32323232....
================
...41......41...
...3........2...
................
................
................
................
................
................
................
...4........1...
...32......32...
================
And so on.
Triangle begins:
1,2,3,4;
1,2,3, 2,3,4, 3,4,1, 4,1,2;
1,2,3, 2,3,4, 3,4,1, 4,1,2;
1,2,3,2,3,4,1,2,3, 2,3,4,3,4,1,2,3,4, 3,4,1,4,1,2,3,4,1, 4,1,2,1,2,3,4,1,2;
1,2,3, 2,3,4, 3,4,1, 4,1,2;
1,2,3,2,3,4,1,2,3, 2,3,4,3,4,1,2,3,4, 3,4,1,4,1,2,3,4,1, 4,1,2,1,2,3,4,1,2;
Contribution from Omar E. Pol, Dec 09 2009: (Start)
Illustration for n = 1..148
================
.41..41..41..41.
.341412..341412.
..3412....3412..
..434141414121..
.43234123412321.
.32.43414121.32.
....32341232....
....41432141....
.41.34323212.41.
.34143214321412.
..343232323212..
..4321....4321..
.432321..432321.
.32..32..32..32.
================
(End)

Crossrefs

Cf. A139250, A139251, A160410, A161411, A171170.

Sequence in context: A322424 A309198 A256914 * A159957 A053840 A010883

Adjacent sequences: A171168 A171169 A171170 * A171172 A171173 A171174

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 04 2009

Status

approved