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

Author

Gus Wiseman, May 08 2019

Keywords

• nonn
• tabf

Examples

			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
		

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.

Programs

Mathematica

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