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A344090
Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, then lexicographically.
6
1, 2, 3, 2, 1, 4, 3, 1, 5, 3, 2, 4, 1, 6, 4, 2, 5, 1, 3, 2, 1, 7, 4, 3, 5, 2, 6, 1, 4, 2, 1, 8, 5, 3, 6, 2, 7, 1, 4, 3, 1, 5, 2, 1, 9, 5, 4, 6, 3, 7, 2, 8, 1, 4, 3, 2, 5, 3, 1, 6, 2, 1, 10, 6, 4, 7, 3, 8, 2, 9, 1, 5, 3, 2, 5, 4, 1, 6, 3, 1, 7, 2, 1, 4, 3, 2, 1
OFFSET
0,2
COMMENTS
The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.
EXAMPLE
Tetrangle begins:
0: ()
1: (1)
2: (2)
3: (3)(21)
4: (4)(31)
5: (5)(32)(41)
6: (6)(42)(51)(321)
7: (7)(43)(52)(61)(421)
8: (8)(53)(62)(71)(431)(521)
9: (9)(54)(63)(72)(81)(432)(531)(621)
MATHEMATICA
Table[Sort[Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, 10}]
CROSSREFS
Starting with reversed partitions gives A026793.
The version for compositions is A124734.
Showing partitions as Heinz numbers gives A246867.
The non-strict version is A334301 (reversed: A036036).
Ignoring length gives A344086 (reversed: A246688).
Same as A344089 with partitions reversed.
The version for revlex instead of lex is A344092.
A026791 reads off lexicographically ordered reversed partitions.
A080577 reads off reverse-lexicographically ordered partitions.
A112798 reads off reversed partitions by Heinz number.
A296150 reads off partitions by Heinz number.
Sequence in context: A280047 A106377 A214573 * A344092 A118457 A319247
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 12 2021
STATUS
approved