A333486 Length of the n-th reversed integer partition in graded reverse-lexicographic order. Partition lengths of A228531.

0, 1, 1, 2, 1, 2, 3, 1, 2, 2, 3, 4, 1, 2, 2, 3, 3, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 7, 1, 2, 2, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 7, 8, 9

Offset: 0

Author

Gus Wiseman, May 23 2020

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  0
  1
  1 2
  1 2 3
  1 2 2 3 4
  1 2 2 3 3 4 5
  1 2 2 3 2 3 3 4 4 5 6
  1 2 2 3 2 3 3 4 3 4 4 5 5 6 7
  1 2 2 2 3 3 4 2 3 3 4 3 4 4 5 4 5 5 6 6 7 8
		

Links

• OEIS Wiki, Orderings of partitions
• Wikiversity, Lexicographic and colexicographic order

Crossrefs

Row lengths are A000041.

The generalization to compositions is A000120.

Row sums are A006128.

The same partition has sum A036042.

The length-sensitive version (sum/length/revlex) is A036043.

The colexicographic version (sum/colex) is A049085.

The same partition has minimum A182715.

The lexicographic version (sum/lex) is A193173.

The tetrangle of these partitions is A228531.

The version for non-reversed partitions is A238966.

The same partition has Heinz number A334436.

Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.

Partitions in lexicographic order (sum/lex) are A193073.

Partitions in colexicographic order (sum/colex) are A211992.

Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.

Cf. A026792, A049085, A080576, A080577, A103921, A112798, A115623, A129129, A331581, A334302, A334435, A334442.

Programs

Mathematica

revlexsort[f_,c_]:=OrderedQ[PadRight[{c,f}]];
Table[Length/@Sort[Reverse/@IntegerPartitions[n],revlexsort],{n,0,8}]