A359897 Number of strict integer partitions of n whose parts have the same mean as median.

0, 1, 1, 2, 2, 3, 4, 4, 4, 7, 6, 6, 10, 7, 10, 13, 11, 9, 20, 10, 20, 18, 21, 12, 30, 24, 28, 27, 30, 15, 73, 16, 37, 43, 45, 67, 74, 19, 55, 71, 126, 21, 150, 22, 75, 225, 78, 24, 183, 126, 245, 192, 132, 27, 284, 244, 403, 303, 120, 30, 828

Offset

0,4

Links

Table of n, a(n) for n=0..60.

Example

The a(1) = 1 through a(9) = 7 partitions:
  (1)  (2)  (3)    (4)    (5)    (6)      (7)    (8)    (9)
            (2,1)  (3,1)  (3,2)  (4,2)    (4,3)  (5,3)  (5,4)
                          (4,1)  (5,1)    (5,2)  (6,2)  (6,3)
                                 (3,2,1)  (6,1)  (7,1)  (7,2)
                                                        (8,1)
                                                        (4,3,2)
                                                        (5,3,1)

Mathematica

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

Crossrefs

The non-strict version is A240219, complement A359894, ranked by A359889.

The complement is counted by A359898.

The odd-length case is A359899, complement A359900.

A000041 counts partitions, strict A000009.

A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.

A008289 counts strict partitions by mean.

A237984 counts partitions containing their mean, complement A327472.

A240850 counts strict partitions containing their mean, complement A240851.

A325347 counts ptns with integer median, strict A359907, ranked by A359908.

Cf. A065795, A066571, A067659, A082550, A102627, A135342, A316313, A327473, A327475, A328966, A359909.

Sequence in context: A210556 A208914 A049980 * A209698 A141525 A209764

Adjacent sequences: A359894 A359895 A359896 * A359898 A359899 A359900

Keyword

nonn

Author

Gus Wiseman, Jan 20 2023

Status

approved