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A325537
Irregular triangle whose rows are the sorted combined parts of all strict integer partitions of n.
3
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
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.
Sequence in context: A116908 A265146 A358136 * A072851 A246688 A103627
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 08 2019
STATUS
approved