A344091 Flattened tetrangle of all finite multisets of positive integers sorted first by sum, then by length, then colexicographically.

1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 4, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 5, 2, 3, 1, 4, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 3, 3, 2, 4, 1, 5, 2, 2, 2, 1, 2, 3, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Gus Wiseman, May 12 2021

Keywords

• nonn
• tabf

Comments

First differs from A334302 for partitions of 9.

The zeroth row contains only the empty partition.

A tetrangle is a sequence of finite triangles.

Examples

			Tetrangle begins:
  0: ()
  1: (1)
  2: (2)(11)
  3: (3)(12)(111)
  4: (4)(22)(13)(112)(1111)
  5: (5)(23)(14)(122)(113)(1112)(11111)
  6: (6)(33)(24)(15)(222)(123)(114)(1122)(1113)(11112)(111111)
		

Links

• Wikiversity, Lexicographic and colexicographic order

Crossrefs

The version for lex instead of colex is A036036.

Starting with reversed partitions gives A036037.

Ignoring length gives A211992 (reversed: A080576).

Same as A334301 with partitions reversed.

The version for revlex instead of colex is A334302.

The Heinz numbers of these partitions are A334433.

The strict case is A344089.

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.

Cf. A000041, A026793, A124734, A185974, A228531, A246688, A296774, A334433, A334435, A334438, A334439, A334441, A334442, A344086, A344090.

Programs

Mathematica

Table[Reverse/@Sort[IntegerPartitions[n]],{n,0,9}]