A344088 Flattened tetrangle of reversed strict integer partitions sorted first by sum, then colexicographically.

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

Offset

0,2

Comments

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

Mathematica

colex[f_, c_]:=OrderedQ[PadRight[{Reverse[f], Reverse[c]}]];
Table[Sort[Reverse/@Select[IntegerPartitions[n], UnsameQ@@#&], colex], {n, 0, 10}]

Crossrefs

Positions of first appearances are A015724.

Triangle sums are A066189.

The non-strict version is A080576.

Taking lex instead of colex gives A246688 (non-reversed: A344086).

The non-reversed version is A344087.

Taking revlex instead of colex gives A344089 (non-reversed: A118457).

A026793 gives reversed strict partitions in A-S order (sum/length/lex).

A319247 sorts strict partitions by Heinz number.

A329631 sorts reversed strict partitions by Heinz number.

A344090 gives strict partitions in A-S order (sum/length/lex).

Cf. A005117, A014466, A209862.

Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344091.

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: A072851 A246688 A103627 * A292595 A269596 A080786

Adjacent sequences: A344085 A344086 A344087 * A344089 A344090 A344091

Keyword

nonn,tabf

Author

Gus Wiseman, May 12 2021

Status

approved