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A360243
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Number of integer partitions of n where the parts have the same mean as the distinct parts.
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14
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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
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OFFSET
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0,3
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Mean[#]==Mean[Union[#]]&]], {n, 0, 30}]
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CROSSREFS
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For multiplicities instead of distinct parts we have A360068.
These partitions have ranks A360247.
A008284 counts partitions by number of parts.
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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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