A344086 Flattened tetrangle of strict integer partitions sorted first by sum, then lexicographically.

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

Mathematica

lexsort[f_, c_]:=OrderedQ[PadRight[{f, c}]];
Table[Sort[Select[IntegerPartitions[n], UnsameQ@@#&], lexsort], {n, 0, 8}]

Crossrefs

Positions of first appearances are A015724.

Triangle sums are A066189.

Taking revlex instead of lex gives A118457.

The not necessarily strict version is A193073.

The version for reversed partitions is A246688.

The Heinz numbers of these partitions grouped by sum are A246867.

The ordered generalization is A339351.

Taking colex instead of lex gives A344087.

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

A319247 sorts reversed strict partitions by Heinz number.

A329631 sorts 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, A211992, A228100, A228351, A228531, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A344085, A344086, A344088, A344089.

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

Sequence in context: A291123 A292594 A093613 * A335933 A344087 A118816

Adjacent sequences: A344083 A344084 A344085 * A344087 A344088 A344089

Keyword

nonn,tabf

Author

Gus Wiseman, May 11 2021

Status

approved