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A338616
a(n) is twice the number of parts in all partitions of n into consecutive parts.
1
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
OFFSET
1,1
COMMENTS
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
FORMULA
a(n) = 2*A204217(n).
EXAMPLE
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.
CROSSREFS
Cf. A054844 (twice the number of partitions of n into consecutive parts), A204217.
Sequence in context: A239074 A160122 A093656 * A174028 A084426 A255049
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 28 2020
STATUS
approved