A344092 Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, and finally reverse-lexicographically.

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

Offset

0,2

Comments

First differs from A118457 at a(53) = 4, A118457(53) = 2.

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

Mathematica

revlensort[f_, c_]:=If[Length[f]!=Length[c], Length[f]<Length[c], OrderedQ[{c, f}]];
Table[Sort[Select[IntegerPartitions[n], UnsameQ@@#&], revlensort], {n, 0, 10}]

Crossrefs

Same as A026793 with rows reversed.

Ignoring length gives A118457.

The non-strict version is A334439 (reversed: A036036/A334302).

The version for lex instead of revlex is A344090.

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. A036037, A036043, A103921, A124734, A185974, A211992, A296774, A334301, A334433, A334435, A334438, A334441.

Sequence in context: A106377 A214573 A344090 * A118457 A319247 A343180

Adjacent sequences: A344089 A344090 A344091 * A344093 A344094 A344095

Keyword

nonn,tabf

Author

Gus Wiseman, May 14 2021

Status

approved