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%I #6 Feb 24 2021 02:48:19
%S 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,
%T 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,
%U 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
%N Corner sequence (starting each round with the corner (SE): 1,2,3).
%C See A161411, which is the main entry for this sequence.
%C See also A171170 for another version.
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%e ================
%e .......41.......
%e .......32.......
%e ================
%e ......4141......
%e ......3..2......
%e ......4..1......
%e ......3232......
%e ================
%e .....41..41.....
%e .....3....2.....
%e ................
%e ................
%e .....4....1.....
%e .....32..32.....
%e ================
%e ....41414141....
%e ....3..23..2....
%e ....4......1....
%e ....32....32....
%e ....41....41....
%e ....3......2....
%e ....4..14..1....
%e ....32323232....
%e ================
%e ...41......41...
%e ...3........2...
%e ................
%e ................
%e ................
%e ................
%e ................
%e ................
%e ................
%e ...4........1...
%e ...32......32...
%e ================
%e And so on.
%e Triangle begins:
%e 1,2,3,4;
%e 1,2,3, 2,3,4, 3,4,1, 4,1,2;
%e 1,2,3, 2,3,4, 3,4,1, 4,1,2;
%e 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;
%e 1,2,3, 2,3,4, 3,4,1, 4,1,2;
%e 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;
%e Contribution from _Omar E. Pol_, Dec 09 2009: (Start)
%e Illustration for n = 1..148
%e ================
%e .41..41..41..41.
%e .341412..341412.
%e ..3412....3412..
%e ..434141414121..
%e .43234123412321.
%e .32.43414121.32.
%e ....32341232....
%e ....41432141....
%e .41.34323212.41.
%e .34143214321412.
%e ..343232323212..
%e ..4321....4321..
%e .432321..432321.
%e .32..32..32..32.
%e ================
%e (End)
%Y Cf. A139250, A139251, A160410, A161411, A171170.
%K nonn,tabf
%O 1,2
%A _Omar E. Pol_, Dec 04 2009