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

0,2

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.

Links

Table of n, a(n) for n=0..76.

Wikiversity, Lexicographic and colexicographic order

Example

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)

Mathematica

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

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.

Sequence in context: A335122 A334442 A036036 * A334302 A228531 A360056

Adjacent sequences: A344088 A344089 A344090 * A344092 A344093 A344094

Keyword

nonn,tabf

Author

Gus Wiseman, May 12 2021

Status

approved