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A334441 Maximum part of the n-th integer partition in Abramowitz-Stegun (sum/length/lex) order; a(0) = 0. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..87.

Wikiversity, Lexicographic and colexicographic order

EXAMPLE

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

MATHEMATICA

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

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.

Sequence in context: A193278 A337632 A057058 * A278104 A141672 A141671

Adjacent sequences: A334438 A334439 A334440 * A334442 A334443 A334444

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, May 06 2020

STATUS

approved

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Last modified December 7 22:27 EST 2022. Contains 358671 sequences. (Running on oeis4.)