A359907 - OEIS

A359907

Number of strict integer partitions of n with integer median.

0, 1, 1, 1, 2, 1, 4, 2, 6, 4, 9, 6, 14, 10, 18, 16, 27, 23, 36, 34, 51, 49, 67, 68, 94, 95, 122, 129, 166, 174, 217, 233, 287, 308, 371, 405, 487, 528, 622, 683, 805, 880, 1024, 1127, 1305, 1435, 1648, 1818, 2086, 2295, 2611, 2882, 3273, 3606, 4076, 4496, 5069

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OFFSET

0,5

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=0..56.

EXAMPLE

The a(1) = 1 through a(14) = 18 partitions (A..E = 10..14):

1 2 3 4 5 6 7 8 9 A B C D E

31 42 421 53 432 64 542 75 643 86

51 62 531 73 632 84 652 95

321 71 621 82 641 93 742 A4

431 91 731 A2 751 B3

521 532 821 B1 832 C2

541 543 841 D1

631 642 931 653

721 651 A21 743

732 6421 752

741 761

831 842

921 851

5421 932

941

A31

B21

7421

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Median[#]]&]], {n, 0, 30}]

CROSSREFS

For mean instead of median: A102627, non-strict A067538 (ranked by A316413).

This is the strict case of A325347, ranked by A359908.

The median statistic is ranked by A360005(n)/2.

A000041 counts partitions, strict A000009.

A051293 counts subsets with integer mean, median A000975, cf. A005578.

A058398 counts partitions by mean, see also A008284, A327482.

A326567/A326568 gives the mean of prime indices.

A359893, A359901, A359902 count partitions by median.

Cf. A000016, A082550, A240219, A240850, A326669, A327475, A328966, A359897.

Sequence in context: A239242 A340621 A008733 * A244515 A154280 A004795

Adjacent sequences: A359904 A359905 A359906 * A359908 A359909 A359910

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 21 2023

STATUS

approved