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A360250
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Number of integer partitions of n where the parts have greater mean than the distinct parts.
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10
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0, 0, 0, 0, 0, 1, 0, 2, 2, 3, 3, 9, 5, 13, 15, 18, 20, 37, 34, 59, 51, 68, 92, 134, 121, 167, 203, 251, 282, 387, 375, 537, 561, 714, 888, 958, 1042, 1408, 1618, 1939, 2076, 2650, 2764, 3479, 3863, 4431, 5387, 6520, 6688, 8098, 9041, 10614, 12084, 14773, 15469
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OFFSET
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0,8
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LINKS
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FORMULA
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EXAMPLE
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The a(5) = 1 through a(12) = 5 partitions:
(221) . (331) (332) (441) (442) (443) (552)
(2221) (22211) (3321) (3331) (551) (4431)
(22221) (222211) (3332) (33321)
(4331) (44211)
(4421) (2222211)
(33221)
(33311)
(222221)
(2222111)
For example, the partition y = (4,3,3,1) has mean 11/4 and distinct parts {1,3,4} with mean 8/5, so y is counted under a(11).
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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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These partitions have ranks A360252.
A008284 counts partitions by number of parts.
A116608 counts partitions by number of distinct parts.
A359894 counts partitions with mean different from median, ranks A359890.
A360071 counts partitions by number of parts and number of distinct parts.
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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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