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A344088
Flattened tetrangle of reversed strict integer partitions sorted first by sum, then colexicographically.
5
1, 2, 1, 2, 3, 1, 3, 4, 2, 3, 1, 4, 5, 1, 2, 3, 2, 4, 1, 5, 6, 1, 2, 4, 3, 4, 2, 5, 1, 6, 7, 1, 3, 4, 1, 2, 5, 3, 5, 2, 6, 1, 7, 8, 2, 3, 4, 1, 3, 5, 4, 5, 1, 2, 6, 3, 6, 2, 7, 1, 8, 9, 1, 2, 3, 4, 2, 3, 5, 1, 4, 5, 1, 3, 6, 4, 6, 1, 2, 7, 3, 7, 2, 8, 1, 9, 10
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: (12)(3)
4: (13)(4)
5: (23)(14)(5)
6: (123)(24)(15)(6)
7: (124)(34)(25)(16)(7)
8: (134)(125)(35)(26)(17)(8)
9: (234)(135)(45)(126)(36)(27)(18)(9)
MATHEMATICA
colex[f_, c_]:=OrderedQ[PadRight[{Reverse[f], Reverse[c]}]];
Table[Sort[Reverse/@Select[IntegerPartitions[n], UnsameQ@@#&], colex], {n, 0, 10}]
CROSSREFS
Positions of first appearances are A015724.
Triangle sums are A066189.
The non-strict version is A080576.
Taking lex instead of colex gives A246688 (non-reversed: A344086).
The non-reversed version is A344087.
Taking revlex instead of colex gives A344089 (non-reversed: A118457).
A026793 gives reversed strict partitions in A-S order (sum/length/lex).
A319247 sorts strict partitions by Heinz number.
A329631 sorts reversed strict partitions by Heinz number.
A344090 gives strict partitions in A-S order (sum/length/lex).
Sequence in context: A072851 A246688 A103627 * A292595 A269596 A080786
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 12 2021
STATUS
approved