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A323651
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Number of elements added at n-th stage to the toothpick structure of A323650.
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8
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1, 2, 4, 8, 4, 8, 12, 24, 4, 8, 12, 24, 12, 24, 36, 72, 4, 8, 12, 24, 12, 24, 36, 72, 12, 24, 36, 72, 36, 72, 108, 216, 4, 8, 12, 24, 12, 24, 36, 72, 12, 24, 36, 72, 36, 72, 108, 216, 12, 24, 36, 72, 36, 72, 108, 216, 36, 72, 108, 216, 108, 216, 324, 648, 4, 8, 12, 24, 12, 24, 36, 72, 12, 24, 36, 72, 36, 72, 108, 216
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OFFSET
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1,2
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COMMENTS
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The odd-indexed terms (a bisection) gives A147582, the first differences of A147562 (Ulam-Warburton cellular automaton).
The even-indexed terms (a bisection) gives A147582 multiplied by 2.
The word of this cellular automaton is "ab", so the structure of the irregular triangle is as shown below:
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;
...
Row lengths are the terms of A011782 multiplied by 2, also the column 2 of A296612.
Columns "a" contain numbers of I-toothpicks. Columns "b" contain numbers of V-toothpicks. See the example.
For further information about the word of cellular automata see A296612.
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LINKS
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FORMULA
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EXAMPLE
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Written as an irregular triangle the sequence begins:
1,2;
4,8;
4,8,12,24;
4,8,12,24,12,24,36,72;
4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216;
4,8,12,24,12,24,36,72,12,24,36,72,36,72,108,216,12,24,36,72,36,72,108,216,...
...
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CROSSREFS
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Cf. A011782, A139250, A139251, A147562, A147582, A160120, A160121, A161206, A161207, A296612, A323641, A323642, A323649.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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