A344089 Flattened tetrangle of reversed strict integer partitions, sorted first by length and then colexicographically.

1, 2, 3, 1, 2, 4, 1, 3, 5, 2, 3, 1, 4, 6, 2, 4, 1, 5, 1, 2, 3, 7, 3, 4, 2, 5, 1, 6, 1, 2, 4, 8, 3, 5, 2, 6, 1, 7, 1, 3, 4, 1, 2, 5, 9, 4, 5, 3, 6, 2, 7, 1, 8, 2, 3, 4, 1, 3, 5, 1, 2, 6, 10, 4, 6, 3, 7, 2, 8, 1, 9, 2, 3, 5, 1, 4, 5, 1, 3, 6, 1, 2, 7, 1, 2, 3, 4

Offset

0,2

Comments

First differs from the revlex (instead of colex) version for partitions of 12.

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..86.

Wikiversity, Lexicographic and colexicographic order

Example

Tetrangle begins:
  0: ()
  1: (1)
  2: (2)
  3: (3)(12)
  4: (4)(13)
  5: (5)(23)(14)
  6: (6)(24)(15)(123)
  7: (7)(34)(25)(16)(124)
  8: (8)(35)(26)(17)(134)(125)
  9: (9)(45)(36)(27)(18)(234)(135)(126)

Mathematica

Table[Reverse/@Sort[Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, 30}]

Crossrefs

Positions of first appearances are A015724 plus one.

Taking lex instead of colex gives A026793 (non-reversed: A118457).

Triangle sums are A066189.

Reversing all partitions gives A344090.

The non-strict version is A344091.

A319247 sorts strict partitions by Heinz number.

A329631 sorts reversed strict partitions by Heinz number.

Cf. A005117, A014466, A209862, A325683, A325859.

Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344087, A344088, A344089.

Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.

Sequence in context: A296656 A303945 A026793 * A329631 A239304 A072193

Adjacent sequences: A344086 A344087 A344088 * A344090 A344091 A344092

Keyword

nonn,tabf

Author

Gus Wiseman, May 12 2021

Status

approved