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A344092
Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, and finally reverse-lexicographically.
1
1, 2, 3, 2, 1, 4, 3, 1, 5, 4, 1, 3, 2, 6, 5, 1, 4, 2, 3, 2, 1, 7, 6, 1, 5, 2, 4, 3, 4, 2, 1, 8, 7, 1, 6, 2, 5, 3, 5, 2, 1, 4, 3, 1, 9, 8, 1, 7, 2, 6, 3, 5, 4, 6, 2, 1, 5, 3, 1, 4, 3, 2, 10, 9, 1, 8, 2, 7, 3, 6, 4, 7, 2, 1, 6, 3, 1, 5, 4, 1, 5, 3, 2, 4, 3, 2, 1
OFFSET
0,2
COMMENTS
First differs from A118457 at a(53) = 4, A118457(53) = 2.
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)(41)(32)
6: (6)(51)(42)(321)
7: (7)(61)(52)(43)(421)
8: (8)(71)(62)(53)(521)(431)
9: (9)(81)(72)(63)(54)(621)(531)(432)
MATHEMATICA
revlensort[f_, c_]:=If[Length[f]!=Length[c], Length[f]<Length[c], OrderedQ[{c, f}]];
Table[Sort[Select[IntegerPartitions[n], UnsameQ@@#&], revlensort], {n, 0, 10}]
CROSSREFS
Same as A026793 with rows reversed.
Ignoring length gives A118457.
The non-strict version is A334439 (reversed: A036036/A334302).
The version for lex instead of revlex is A344090.
A026791 reads off lexicographically ordered reversed partitions.
A080577 reads off reverse-lexicographically ordered partitions.
A112798 reads off reversed partitions by Heinz number.
A193073 reads off lexicographically ordered partitions.
A296150 reads off partitions by Heinz number.
Sequence in context: A106377 A214573 A344090 * A118457 A319247 A343180
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, May 14 2021
STATUS
approved