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1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 5, 16, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 6, 32, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 5, 16, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 7, 64
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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 to the toothpick structure (related to integer compositions) of A228370.
The equivalent sequence for integer partitions is A220517.
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LINKS
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FORMULA
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EXAMPLE
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Illustration of the structure after 32 stages. The diagram represents the 16 compositions of 5. The k-th horizontal line segment has length A001511(k) equals the largest part of the k-th region. The k-th vertical line segment has length A006519(k) equals the number of parts of the k-th region.
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16 _ |
15 _|_ |
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11 _|_ | |
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9 _|_|_|_ |
8 _ | |
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3 _|_ | | |
2 _ | | | |
1 | | | | |
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Written as an irregular triangle the sequence begins:
1,1;
2,2;
1,1,3,4;
1,1,2,2,1,1,4,8;
1,1,2,2,1,1,3,4,1,1,2,2,1,1,5,16;
1,1,2,2,1,1,3,4,1,1,2,2,1,1,4,8,1,1,2,2,1,1,3,4,1,1,2,2,1,1,6,32;
...
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PROG
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(Python)
def A228371(n): return ((m:=(n>>1)+1)&-m).bit_length() if n&1 else (m:=n>>1)&-m # Chai Wah Wu, Jul 14 2022
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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