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A170905
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Consider the hexagonal cellular automaton defined in A151723, A151724; a(n) = number of cells that go from OFF to ON at stage n, if we only look at a 60-degree wedge (including the two bounding edges).
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13
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0, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 6, 10, 10, 8, 14, 16, 2, 4, 6, 10, 10, 10, 18, 26, 18, 8, 14, 24, 28, 20, 32, 32, 2, 4, 6, 10, 10, 10, 18, 26, 18, 10, 18, 30, 38, 34, 42, 58, 34, 8, 14, 24, 28, 28, 44, 68, 60, 28, 32, 56, 70, 50, 70, 64, 2, 4, 6, 10, 10, 10, 18, 26, 18, 10, 18, 30, 38, 34, 42
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..1025
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
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FORMULA
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a(n) = A170898(n-2) + 1 for n >= 2.
a(n) = 2*A169778(n) for n != 1.
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EXAMPLE
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From Omar E. Pol, Feb 12 2013: (Start)
When written as a triangle starting from 1, the right border gives A000079 and row lengths give A011782.
1;
2;
2,4;
2,4,6,8;
2,4,6,10,10,8,14,16;
2,4,6,10,10,10,18,26,18,8,14,24,28,20,32,32;
2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,58,34,8,14,24,28,28,44,68,60,28,32,56,70,50,70,64;
2,4,6,10,10,10,18,26,18,10,18,30,38,34,42,...
... (End)
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CROSSREFS
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Cf. A151723, A151724, A170898, A169778, A169780 (partial sums).
Sequence in context: A233765 A233781 A233971 * A233761 A035096 A066675
Adjacent sequences: A170902 A170903 A170904 * A170906 A170907 A170908
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, Jan 22 2010
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STATUS
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approved
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