A325537 Irregular triangle whose rows are the sorted combined parts of all strict integer partitions of n.

1, 2, 1, 2, 3, 1, 3, 4, 1, 2, 3, 4, 5, 1, 1, 2, 2, 3, 4, 5, 6, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 10

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Example

The strict integer partitions of 6 are {(6), (5,1), (4,2), (3,2,1)} with multiset union {1,1,2,2,3,4,5,6}, which is row n = 6.
Triangle begins:
  1
  2
  1 2 3
  1 3 4
  1 2 3 4 5
  1 1 2 2 3 4 5 6
  1 1 2 2 3 4 4 5 6 7
  1 1 1 2 2 3 3 4 5 5 6 7 8
  1 1 1 2 2 2 3 3 3 4 4 5 5 6 6 7 8 9

Mathematica

Table[Sort[Join@@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 10}]

Crossrefs

Row lengths are A015723.

Row sums are A066189.

Row products are A325504.

Run-lengths of row n are row n of A325513.

Cf. A000009, A006128, A022629, A181821, A302247, A325515.

Sequence in context: A116908 A265146 A358136 * A072851 A246688 A103627

Adjacent sequences: A325534 A325535 A325536 * A325538 A325539 A325540

Keyword

nonn,tabf

Author

Gus Wiseman, May 08 2019

Status

approved