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A361800
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Number of integer partitions of n with the same length as median.
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3
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1, 0, 0, 2, 0, 0, 1, 2, 3, 3, 3, 3, 4, 6, 9, 13, 14, 15, 18, 21, 27, 32, 40, 46, 55, 62, 72, 82, 95, 111, 131, 157, 186, 225, 264, 316, 366, 430, 495, 578, 663, 768, 880, 1011, 1151, 1316, 1489, 1690, 1910, 2158, 2432, 2751, 3100, 3505, 3964, 4486, 5079, 5764
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OFFSET
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1,4
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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(1) = 1 through a(15) = 9 partitions (A=10, B=11):
1 . . 22 . . 331 332 333 433 533 633 733 833 933
31 431 432 532 632 732 832 932 A32
531 631 731 831 931 A31 B31
4441 4442 4443
5441 5442
5531 5532
6441
6531
6621
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[#]==Median[#]&]], {n, 30}]
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CROSSREFS
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For minimum instead of median we have A006141, for twice minimum A237757.
For maximum instead of median we have A047993, for twice length A237753.
For maximum instead of length we have A053263, for twice median A361849.
For mean instead of median we have A206240 (zeros removed).
For minimum instead of length we have A361860.
A000975 counts subsets with integer median.
A360005 gives twice median of prime indices.
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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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