A171170 Corner sequence (starting each round in the first quadrant).

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

Offset

1,2

Comments

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

See also A171171 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;
4,1,2, 1,2,3, 2,3,4, 3,4,1;
4,1,2, 1,2,3, 2,3,4, 3,4,1;
3,4,1,4,1,2,1,2,3, 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;
4,1,2, 1,2,3, 2,3,4, 3,4,1;
3,4,1,4,1,2,1,2,3, 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;
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, A171171.

Sequence in context: A134581 A099587 A172160 * A256913 A346617 A160386

Adjacent sequences: A171167 A171168 A171169 * A171171 A171172 A171173

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 04 2009

Status

approved