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A338616
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a(n) is twice the number of parts in all partitions of n into consecutive parts.
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1
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2, 2, 6, 2, 6, 8, 6, 2, 12, 10, 6, 8, 6, 10, 22, 2, 6, 16, 6, 12, 24, 10, 6, 8, 16, 10, 24, 16, 6, 26, 6, 2, 24, 10, 30, 24, 6, 10, 24, 12, 6, 30, 6, 18, 52, 10, 6, 8, 20, 20, 24, 18, 6, 34, 36, 16, 24, 10, 6, 34, 6, 10, 56, 2, 36, 38, 6, 18, 24, 34, 6, 26, 6, 10, 54, 18, 42, 40, 6, 12
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OFFSET
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1,1
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COMMENTS
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a(n) = 6 if and only if n is an odd prime.
a(n) = 2 if and only if n is a power of 2. - Omar E. Pol, Dec 13 2021
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LINKS
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FORMULA
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EXAMPLE
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Illustration of initial terms:
Diagram
n a(n) _ _
1 2 _|1 1|_
2 2 _|1 _ _ 1|_
3 6 _|1 |2 2| 1|_
4 2 _|1 _| |_ 1|_
5 6 _|1 |2 _ _ 2| 1|_
6 8 _|1 _| |3 3| |_ 1|_
7 6 _|1 |2 | | 2| 1|_
8 2 _|1 _| _| |_ |_ 1|_
9 12 _|1 |2 |3 _ _ 3| 2| 1|_
10 10 _|1 _| | |4 4| | |_ 1|_
11 6 _|1 |2 _| | | |_ 2| 1|_
12 8 _|1 _| |3 | | 3| |_ 1|_
13 6 _|1 |2 | _| |_ | 2| 1|_
14 10 _|1 _| _| |4 _ _ 4| |_ |_ 1|_
15 22 _|1 |2 |3 | |5 5| | 3| 2| 1|_
16 2 |1 | | | | | | | | 1|
...
a(n) is the total length of all vertical line segments that are below and that share one vertex with the horizontal line segments that are in the n-th level of the diagram.
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CROSSREFS
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Cf. A054844 (twice the number of partitions of n into consecutive parts), A204217.
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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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