A344090 Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, then lexicographically.

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

Author

Gus Wiseman, May 12 2021

Keywords

• nonn
• tabf

Comments

The zeroth row contains only the empty partition.

A tetrangle is a sequence of finite triangles.

Examples

			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)
		

Links

• Wikiversity, Lexicographic and colexicographic order

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.

Cf. A036037, A036043, A103921, A185974, A193073, A211992, A296774, A334302, A334433, A334435, A334438, A334439, A334440, A334441, A334442, A344091.

Programs

Mathematica

Table[Sort[Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,10}]