A359898 Number of strict integer partitions of n whose parts do not have the same mean as median.

0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 4, 6, 5, 11, 12, 14, 21, 29, 26, 44, 44, 58, 68, 92, 92, 118, 137, 165, 192, 241, 223, 324, 353, 405, 467, 518, 594, 741, 809, 911, 987, 1239, 1276, 1588, 1741, 1823, 2226, 2566, 2727, 3138, 3413, 3905, 4450, 5093, 5434, 6134

Offset

0,9

Links

Table of n, a(n) for n=0..55.

Example

The a(7) = 1 through a(13) = 11 partitions:
  (4,2,1)  (4,3,1)  (6,2,1)  (5,3,2)  (5,4,2)    (6,5,1)    (6,4,3)
           (5,2,1)           (5,4,1)  (6,3,2)    (7,3,2)    (6,5,2)
                             (6,3,1)  (6,4,1)    (8,3,1)    (7,4,2)
                             (7,2,1)  (7,3,1)    (9,2,1)    (7,5,1)
                                      (8,2,1)    (6,3,2,1)  (8,3,2)
                                      (5,3,2,1)             (8,4,1)
                                                            (9,3,1)
                                                            (10,2,1)
                                                            (5,4,3,1)
                                                            (6,4,2,1)
                                                            (7,3,2,1)

Mathematica

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

Crossrefs

The non-strict version is ranked by A359890, complement A359889.

The non-strict version is A359894, complement A240219.

The complement is counted by A359897.

The odd-length case is A359900, complement A359899.

A000041 counts partitions, strict A000009.

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

A008289 counts strict partitions by mean.

A067538 counts ptns with integer mean, strict A102627, ranked by A316413.

A237984 counts ptns containing their mean, strict A240850, ranked by A327473.

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

A359893 and A359901 count partitions by median, odd-length A359902.

Cf. A000016, A065795, A066571, A082550, A135342, A240851, A327475, A327482, A328966, A359906.

Sequence in context: A134306 A006265 A131452 * A335920 A111104 A026190

Adjacent sequences: A359895 A359896 A359897 * A359899 A359900 A359901

Keyword

nonn

Author

Gus Wiseman, Jan 20 2023

Status

approved