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

Author

Gus Wiseman, May 14 2021

Keywords

• nonn
• tabf

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.

Examples

			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)
		

Links

• Wikiversity, Lexicographic and colexicographic order

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.

Programs

Mathematica

revlensort[f_,c_]:=If[Length[f]!=Length[c],Length[f]