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A340385 Number of integer partitions of n into an odd number of parts, the greatest of which is odd. 18
1, 0, 2, 0, 3, 1, 6, 3, 10, 7, 18, 15, 30, 28, 51, 50, 82, 87, 134, 145, 211, 235, 331, 375, 510, 586, 779, 901, 1172, 1366, 1750, 2045, 2581, 3026, 3778, 4433, 5476, 6430, 7878, 9246, 11240, 13189, 15931, 18670, 22417, 26242, 31349, 36646, 43567, 50854 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

The a(3) = 2 through a(10) = 7 partitions:

  3     5       321   7         332     9           532

  111   311           322       521     333         541

        11111         331       32111   522         721

                      511               531         32221

                      31111             711         33211

                      1111111           32211       52111

                                        33111       3211111

                                        51111

                                        3111111

                                        111111111

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]*Max[#]]&]], {n, 30}]

CROSSREFS

Partitions of odd length are counted by A027193, ranked by A026424.

Partitions with odd maximum are counted by A027193, ranked by A244991.

The Heinz numbers of these partitions are given by A340386.

Other cases of odd length:

- A024429 counts set partitions of odd length.

- A067659 counts strict partitions of odd length.

- A089677 counts ordered set partitions of odd length.

- A166444 counts compositions of odd length.

- A174726 counts ordered factorizations of odd length.

- A332304 counts strict compositions of odd length.

- A339890 counts factorizations of odd length.

A000009 counts partitions into odd parts, ranked by A066208.

A026804 counts partitions whose least part is odd.

A058695 counts partitions of odd numbers, ranked by A300063.

A072233 counts partitions by sum and length.

A101707 counts partitions with odd rank.

A160786 counts odd-length partitions of odd numbers, ranked by A300272.

A340101 counts factorizations into odd factors.

A340102 counts odd-length factorizations into odd factors.

Cf. A000700, A027187, A078408, A174725, A236914.

Sequence in context: A130627 A006209 A005307 * A143351 A350962 A241644

Adjacent sequences:  A340382 A340383 A340384 * A340386 A340387 A340388

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 08 2021

STATUS

approved

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Last modified May 19 23:40 EDT 2022. Contains 353847 sequences. (Running on oeis4.)