A297626 Triangle read by rows in which row n gives a partition of n with the most subpartitions.

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

Offset: 1

Author

Brian Hopkins, Jan 04 2018

Keywords

• nonn
• tabf

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A116480, A117500.