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A160407
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First differences of toothpick numbers A160406.
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20
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1, 1, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 4, 6, 10, 8, 2, 2, 4, 4, 4, 6, 10, 8, 4, 6, 10, 10, 12, 20, 26, 16, 2, 2, 4, 4, 4, 6, 10, 8, 4, 6, 10, 10, 12, 20, 26, 16, 4, 6, 10, 10, 12, 20, 26, 18, 12, 20, 28, 30, 42
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OFFSET
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1,3
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COMMENTS
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Number of toothpicks added at n-th stage in the toothpick structure of A160406.
From Omar E. Pol, Mar 15 2020: (Start)
The cellular automaton described in A160406 has word "ab", so the structure of this triangle is as follows:
a,b;
a,b;
a,b,a,b;
a,b,a,b,a,b,a,b;
a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
...
The row lengths are the terms of A011782 multiplied by 2, equaling the column 2 of the square array A296612: 2, 2, 4, 8, 16, ...
This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks that are parallel to initial toothpick, and the even-indexed columns (b) contain numbers of the toothpicks that are orthogonal to the initial toothpick.
For further information about the "word" of a cellular automaton see A296612. (End)
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LINKS
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Table of n, a(n) for n=1..61.
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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EXAMPLE
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From Omar E. Pol, Jul 18 2009, Mar 15 2020: (Start)
If written as a triangle:
1,1;
2,2;
2,2,4,4;
2,2,4,4,4,6,10,8;
2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16;
2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16,4,6,10,10,12,20,26,18,12,20,28,30,42;...
(End)
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CROSSREFS
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Cf. A011782, A139250, A139251, A153000, A153006, A152980, A160406, A161830, A161831, A296612.
Sequence in context: A051464 A151565 A060632 * A007457 A119802 A237120
Adjacent sequences: A160404 A160405 A160406 * A160408 A160409 A160410
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KEYWORD
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nonn,changed
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AUTHOR
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Omar E. Pol, May 23 2009
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EXTENSIONS
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More terms from N. J. A. Sloane, Jul 17 2009
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STATUS
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approved
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