

A334441


Maximum part of the nth integer partition in AbramowitzStegun (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
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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 AbramowitzStegun (sum/length/lex) order are A036036.
Partitions in increasinglength colex order (sum/length/colex) are A036037.
Graded reverselexicographically 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 AbramowitzStegun (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



