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

0,4

Links

Table of n, a(n) for n=0..96.

OEIS Wiki, Orderings of partitions

Wikiversity, Lexicographic and colexicographic order

Example

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

Mathematica

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

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.

Sequence in context: A333518 A252230 A036043 * A128628 A238966 A353510

Adjacent sequences: A333483 A333484 A333485 * A333487 A333488 A333489

Keyword

nonn,tabf

Author

Gus Wiseman, May 23 2020

Status

approved