A338616 a(n) is twice the number of parts in all partitions of n into consecutive parts.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to partitions

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.

Cf. A000079, A001227, A065091, A237591, A237593, A286001, A335616.

Sequence in context: A239074 A160122 A093656 * A174028 A084426 A255049

Adjacent sequences: A338613 A338614 A338615 * A338617 A338618 A338619

Keyword

nonn

Author

Omar E. Pol, Nov 28 2020

Status

approved