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A359897
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Number of strict integer partitions of n whose parts have the same mean as median.
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21
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0, 1, 1, 2, 2, 3, 4, 4, 4, 7, 6, 6, 10, 7, 10, 13, 11, 9, 20, 10, 20, 18, 21, 12, 30, 24, 28, 27, 30, 15, 73, 16, 37, 43, 45, 67, 74, 19, 55, 71, 126, 21, 150, 22, 75, 225, 78, 24, 183, 126, 245, 192, 132, 27, 284, 244, 403, 303, 120, 30, 828
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OFFSET
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0,4
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LINKS
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EXAMPLE
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The a(1) = 1 through a(9) = 7 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(2,1) (3,1) (3,2) (4,2) (4,3) (5,3) (5,4)
(4,1) (5,1) (5,2) (6,2) (6,3)
(3,2,1) (6,1) (7,1) (7,2)
(8,1)
(4,3,2)
(5,3,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Mean[#]==Median[#]&]], {n, 0, 30}]
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CROSSREFS
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The complement is counted by A359898.
A008289 counts strict partitions by mean.
A240850 counts strict partitions containing their mean, complement A240851.
Cf. A065795, A066571, A067659, A082550, A102627, A135342, A316313, A327473, A327475, A328966, A359909.
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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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