A344087 Flattened tetrangle of strict integer partitions sorted first by sum, then colexicographically.

1, 2, 2, 1, 3, 3, 1, 4, 4, 1, 3, 2, 5, 3, 2, 1, 5, 1, 4, 2, 6, 4, 2, 1, 6, 1, 5, 2, 4, 3, 7, 5, 2, 1, 4, 3, 1, 7, 1, 6, 2, 5, 3, 8, 6, 2, 1, 5, 3, 1, 8, 1, 4, 3, 2, 7, 2, 6, 3, 5, 4, 9, 4, 3, 2, 1, 7, 2, 1, 6, 3, 1, 5, 4, 1, 9, 1, 5, 3, 2, 8, 2, 7, 3, 6, 4, 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: (21)(3)
  4: (31)(4)
  5: (41)(32)(5)
  6: (321)(51)(42)(6)
  7: (421)(61)(52)(43)(7)
  8: (521)(431)(71)(62)(53)(8)
  9: (621)(531)(81)(432)(72)(63)(54)(9)

Mathematica

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

Crossrefs

Positions of first appearances are A015724.

Triangle sums are A066189.

Taking revlex instead of colex gives A118457.

The not necessarily strict version is A211992.

Taking lex instead of colex gives A344086.

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, A080576, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A319247, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344088, A344089, 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: A093613 A344086 A335933 * A118816 A283904 A097289

Adjacent sequences: A344084 A344085 A344086 * A344088 A344089 A344090

Keyword

nonn,tabf

Author

Gus Wiseman, May 11 2021

Status

approved