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

1,2

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