A359896 Number of odd-length integer partitions of n whose parts do not have the same mean as median.

0, 0, 0, 0, 1, 2, 2, 6, 9, 11, 15, 27, 32, 50, 58, 72, 112, 149, 171, 246, 286, 359, 477, 630, 773, 941, 1181, 1418, 1749, 2289, 2668, 3429, 4162, 4878, 6074, 7091, 8590, 10834, 12891, 15180, 18491, 22314, 25845, 31657, 36394, 42269, 52547, 62414, 73576, 85701

Offset

0,6

Links

Table of n, a(n) for n=0..49.

Example

The a(4) = 1 through a(9) = 11 partitions:
  (211)  (221)  (411)    (322)    (332)      (441)
         (311)  (21111)  (331)    (422)      (522)
                         (421)    (431)      (621)
                         (511)    (521)      (711)
                         (22111)  (611)      (22221)
                         (31111)  (22211)    (32211)
                                  (32111)    (33111)
                                  (41111)    (42111)
                                  (2111111)  (51111)
                                             (2211111)
                                             (3111111)

Mathematica

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

Crossrefs

These partitions are ranked by A359892.

The any-length version is A359894, complement A240219, strict A359898.

The complement is counted by A359895, ranked by A359891.

The strict case is A359900, complement A359899.

A000041 counts partitions, strict A000009.

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

A027193 counts odd-length partitions, strict A067659, ranked by A026424.

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. A008289, A066571, A316313, A327472, A327482, A359890, A359906, A359910.

Sequence in context: A371400 A188808 A021819 * A339426 A000021 A367718

Adjacent sequences: A359893 A359894 A359895 * A359897 A359898 A359899

Keyword

nonn

Author

Gus Wiseman, Jan 20 2023

Status

approved