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A361849
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Number of integer partitions of n such that the maximum is twice the median.
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24
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0, 0, 0, 1, 1, 1, 4, 3, 4, 7, 9, 9, 15, 16, 20, 26, 34, 37, 50, 55, 68, 86, 103, 117, 145, 168, 201, 236, 282, 324, 391, 449, 525, 612, 712, 818, 962, 1106, 1278, 1470, 1698, 1939, 2238, 2550, 2924, 3343, 3824, 4341, 4963, 5627, 6399, 7256, 8231, 9300
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OFFSET
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1,7
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COMMENTS
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The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
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LINKS
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EXAMPLE
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The a(4) = 1 through a(11) = 9 partitions:
211 2111 21111 421 422 4221 631 632
3211 221111 4311 4222 5321
22111 2111111 2211111 42211 5411
211111 21111111 322111 42221
2221111 43211
22111111 332111
211111111 22211111
221111111
2111111111
For example, the partition (3,2,1,1) has maximum 3 and median 3/2, so is counted under a(7).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Max@@#==2*Median[#]&]], {n, 30}]
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CROSSREFS
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For minimum instead of median we have A118096.
For length instead of median we have A237753.
For mean instead of median we have A361853.
These partitions have ranks A361856.
For "greater" instead of "equal" we have A361857, allowing equality A361859.
A361860 counts partitions with minimum equal to median.
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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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