A361800 - OEIS

A361800

Number of integer partitions of n with the same length as median.

1, 0, 0, 2, 0, 0, 1, 2, 3, 3, 3, 3, 4, 6, 9, 13, 14, 15, 18, 21, 27, 32, 40, 46, 55, 62, 72, 82, 95, 111, 131, 157, 186, 225, 264, 316, 366, 430, 495, 578, 663, 768, 880, 1011, 1151, 1316, 1489, 1690, 1910, 2158, 2432, 2751, 3100, 3505, 3964, 4486, 5079, 5764

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

The a(1) = 1 through a(15) = 9 partitions (A=10, B=11):

1 . . 22 . . 331 332 333 433 533 633 733 833 933

31 431 432 532 632 732 832 932 A32

531 631 731 831 931 A31 B31

4441 4442 4443

5441 5442

5531 5532

6441

6531

6621

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Length[#]==Median[#]&]], {n, 30}]

CROSSREFS

For minimum instead of median we have A006141, for twice minimum A237757.

For maximum instead of median we have A047993, for twice length A237753.

For maximum instead of length we have A053263, for twice median A361849.

For mean instead of median we have A206240 (zeros removed).

For minimum instead of length we have A361860.

For twice median we have A362049, ranks A362050.

A000041 counts integer partitions, strict A000009.

A000975 counts subsets with integer median.

A325347 counts partitions with integer median, complement A307683.

A359893 and A359901 count partitions by median.

A360005 gives twice median of prime indices.

Cf. A008284, A013580, A027193, A079309, A240219, A362048.

Sequence in context: A146164 A263141 A051510 * A340958 A320781 A284608

Adjacent sequences: A361797 A361798 A361799 * A361801 A361802 A361803

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 07 2023

STATUS

approved