A360243 - OEIS

A360243

Number of integer partitions of n where the parts have the same mean as the distinct parts.

1, 1, 2, 3, 4, 4, 8, 6, 11, 11, 17, 13, 28, 19, 32, 40, 48, 39, 71, 55, 103, 105, 110, 105, 197, 170, 195, 237, 319, 257, 462, 341, 515, 543, 584, 784, 1028, 761, 973, 1153, 1606, 1261, 2137, 1611, 2368, 2815, 2575, 2591, 4393, 3798, 4602, 4663, 5777, 5121

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

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..53.

EXAMPLE

The a(1) = 1 through a(8) = 11 partitions:

(1) (2) (3) (4) (5) (6) (7) (8)

(11) (21) (22) (32) (33) (43) (44)

(111) (31) (41) (42) (52) (53)

(1111) (11111) (51) (61) (62)

(222) (421) (71)

(321) (1111111) (431)

(2211) (521)

(111111) (2222)

(3221)

(3311)

(11111111)

MATHEMATICA

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

CROSSREFS

For multiplicities instead of distinct parts we have A360068.

The complement is counted by A360242, ranks A360246.

For median instead of mean we have A360245, complement A360244.

These partitions have ranks A360247.

Cf. A360250 and A360251, ranks A360252 and A360253.

A000041 counts integer partitions, strict A000009.

A008284 counts partitions by number of parts.

A058398 counts partitions by mean, also A327482.

A067538 counts partitions with integer mean, strict A102627, ranks A316413.

A116608 counts partitions by number of distinct parts.

A360071 counts partitions by number of parts and number of distinct parts.

A360241 counts partitions whose distinct parts have integer mean.

Cf. A051293, A067340, A240219, A316313, A326567/A326568, A326619/A326620, A326621, A349156, A360069.

Sequence in context: A240219 A028298 A047966 * A360683 A317085 A236543

Adjacent sequences: A360240 A360241 A360242 * A360244 A360245 A360246

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 04 2023

STATUS

approved