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A360241
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Number of integer partitions of n whose distinct parts have integer mean.
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16
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0, 1, 2, 2, 4, 3, 8, 6, 13, 13, 22, 19, 43, 34, 56, 66, 97, 92, 156, 143, 233, 256, 322, 341, 555, 542, 710, 831, 1098, 1131, 1644, 1660, 2275, 2484, 3035, 3492, 4731, 4848, 6063, 6893, 8943, 9378, 12222, 13025, 16520, 18748, 22048, 24405, 31446, 33698, 41558
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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) = 13 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (311) (33) (331) (44)
(31) (11111) (42) (511) (53)
(1111) (51) (3211) (62)
(222) (31111) (71)
(321) (1111111) (422)
(3111) (2222)
(111111) (3221)
(3311)
(5111)
(32111)
(311111)
(11111111)
For example, the partition (32111) has distinct parts {1,2,3} with mean 2, so is counted under a(8).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[Union[#]]]&]], {n, 0, 30}]
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CROSSREFS
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For parts instead of distinct parts we have A067538, ranked by A316413.
These partitions are ranked by A326621.
For multiplicities instead of distinct parts: A360069, ranked by A067340.
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.
The following count partitions:
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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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