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A171171
Corner sequence (starting each round with the corner (SE): 1,2,3).
1
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
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.]
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
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 04 2009
STATUS
approved