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A297626 Triangle read by rows in which row n gives a partition of n with the most subpartitions. 0
1, 2, 2, 1, 3, 1, 3, 1, 1, 3, 2, 1, 4, 2, 1, 4, 2, 1, 1, 5, 2, 1, 1, 5, 3, 1, 1, 5, 3, 2, 1, 5, 3, 2, 1, 1, 6, 3, 2, 1, 1, 6, 3, 2, 1, 1, 1, 6, 4, 2, 1, 1, 1, 6, 4, 2, 2, 1, 1, 6, 4, 3, 2, 1, 1, 7, 4, 3, 2, 1, 1, 7, 4, 3, 2, 1, 1, 1, 7, 5, 3, 2, 1, 1, 1, 8, 5, 3, 2, 1, 1, 1, 8, 5, 3, 2, 2, 1, 1, 8, 5, 3, 2, 2, 1, 1, 1, 9, 5, 3, 2, 2, 1, 1, 1, 8, 5, 4, 3, 2, 1, 1, 1, 9, 5, 4, 3, 2, 1, 1, 1, 9, 6, 4, 3, 2, 1, 1, 1, 9, 6, 4, 3, 2, 1, 1, 1, 1, 9, 6, 4, 3, 2, 2, 1, 1, 1, 10, 6, 4, 3, 2, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A partition and its conjugate have the same number of subpartitions; in the case of ties, we take the lexicographically earliest partition.

LINKS

Table of n, a(n) for n=1..166.

Mathoverflow, Upper bound for number of subpartitions of a partition, posted Sep 16 2017

EXAMPLE

Triangle begins

1

2

2 1

3 1

3 1 1

3 2 1

4 2 1

4 2 1 1

5 2 1 1

5 3 1 1

5 3 2 1

5 3 2 1 1

6 3 2 1 1

6 3 2 1 1 1

6 4 2 1 1 1

6 4 2 2 1 1

6 4 3 2 1 1

7 4 3 2 1 1

7 4 3 2 1 1 1

7 5 3 2 1 1 1

8 5 3 2 1 1 1

8 5 3 2 2 1 1

8 5 3 2 2 1 1 1

9 5 3 2 2 1 1 1

8 5 4 3 2 1 1 1

9 5 4 3 2 1 1 1

9 6 4 3 2 1 1 1

9 6 4 3 2 1 1 1 1

9 6 4 3 2 2 1 1 1

CROSSREFS

Cf. A116480, A117500.

Sequence in context: A070786 A255542 A117500 * A206441 A175245 A167413

Adjacent sequences:  A297623 A297624 A297625 * A297627 A297628 A297629

KEYWORD

nonn,tabf

AUTHOR

Brian Hopkins, Jan 04 2018

STATUS

approved

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Last modified March 20 23:22 EDT 2019. Contains 321354 sequences. (Running on oeis4.)