STATUS
proposed
approved
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Revision History for A360243
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Number of integer partitions of n where the parts have the same mean as the distinct parts.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
Number of integer partitions of n where the parts have the same mean as the distinct parts.
CROSSREFS
The complement is counted by A360242, ranked by ranks A360246.
These partitions are ranked by have ranks A360247.
Cf. A360250 and A360251, ranked by ranks A360252 and A360253.
A067538 = counts partitions with integer mean, strict A102627, ranked by ranks A316413.
Cf. A051293, A067340, A240219, `A316313, A326567/A326568, A326619/A326620, `A326621, `A327475, A349156, `A360069.
NAME
allocated for Gus WisemanNumber of integer partitions where the parts have the same mean as the distinct parts.
DATA
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
OFFSET
0,3
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, ranked by A360246.
For median instead of mean we have A360245, complement A360244.
These partitions are ranked by A360247.
Cf. A360250 and A360251, ranked by A360252 and A360253.
A000041 counts integer partitions, strict A000009.
A008284 counts partitions by number of parts.
A058398 counts partitions by mean, also A327482.
A067538 = partitions with integer mean, strict A102627, ranked by 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. A067340, A240219, `A316313, A326567/A326568, A326619/A326620, `A326621, `A327475, A349156, `A360069.
KEYWORD
allocated
nonn
AUTHOR
Gus Wiseman, Feb 04 2023
STATUS
approved
editing
NAME
allocated for Gus Wiseman
KEYWORD
allocated
STATUS
approved