

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
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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 oddlength partitions of odd numbers, ranked by A300272.
A340101 counts factorizations into odd factors.
A340102 counts oddlength 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



