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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 11:39 EDT 2022. Contains 357270 sequences. (Running on oeis4.)