A334441 Maximum part of the n-th integer partition in Abramowitz-Stegun (sum/length/lex) order; a(0) = 0.

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

Offset: 0

Author

Gus Wiseman, May 06 2020

Keywords

• nonn
• tabf

Comments

First differs from A049085 at a(8) = 2, A049085(8) = 3.

The parts of a partition are read in the usual (weakly decreasing) order. The version for reversed (weakly increasing) partitions is A049085.

Examples

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

Links

• Wikiversity, Lexicographic and colexicographic order

Crossrefs

Row lengths are A000041.

The length of the same partition is A036043.

Ignoring partition length (sum/lex) gives A036043 also.

The version for reversed partitions is A049085.

a(n) is the maximum element in row n of A334301.

The number of distinct parts in the same partition is A334440.

Lexicographically ordered reversed partitions are A026791.

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

Partitions in increasing-length colex order (sum/length/colex) are A036037.

Graded reverse-lexicographically ordered partitions are A080577.

Partitions counted by sum and number of distinct parts are A116608.

Graded lexicographically ordered partitions are A193073.

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

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

Cf. A001221, A103921, A124734, A185974, A296774, A299755, A334302, A334433, A334434, A334435, A334438.

Programs

Mathematica

Table[If[n==0,{0},Max/@Sort[IntegerPartitions[n]]],{n,0,10}]