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A344089
Flattened tetrangle of reversed strict integer partitions, sorted first by length and then colexicographically.
8
1, 2, 3, 1, 2, 4, 1, 3, 5, 2, 3, 1, 4, 6, 2, 4, 1, 5, 1, 2, 3, 7, 3, 4, 2, 5, 1, 6, 1, 2, 4, 8, 3, 5, 2, 6, 1, 7, 1, 3, 4, 1, 2, 5, 9, 4, 5, 3, 6, 2, 7, 1, 8, 2, 3, 4, 1, 3, 5, 1, 2, 6, 10, 4, 6, 3, 7, 2, 8, 1, 9, 2, 3, 5, 1, 4, 5, 1, 3, 6, 1, 2, 7, 1, 2, 3, 4
OFFSET
0,2
COMMENTS
First differs from the revlex (instead of colex) version for partitions of 12.
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)(12)
4: (4)(13)
5: (5)(23)(14)
6: (6)(24)(15)(123)
7: (7)(34)(25)(16)(124)
8: (8)(35)(26)(17)(134)(125)
9: (9)(45)(36)(27)(18)(234)(135)(126)
MATHEMATICA
Table[Reverse/@Sort[Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, 30}]
CROSSREFS
Positions of first appearances are A015724 plus one.
Taking lex instead of colex gives A026793 (non-reversed: A118457).
Triangle sums are A066189.
Reversing all partitions gives A344090.
The non-strict version is A344091.
A319247 sorts strict partitions by Heinz number.
A329631 sorts reversed strict partitions by Heinz number.
Sequence in context: A296656 A303945 A026793 * A329631 A239304 A072193
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 12 2021
STATUS
approved