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A361854
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Number of strict integer partitions of n such that (length) * (maximum) = 2n.
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4
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0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 0, 5, 0, 6, 3, 5, 0, 11, 6, 8, 7, 10, 0, 36, 0, 14, 16, 16, 29, 43, 0, 21, 36, 69, 0, 97, 0, 35, 138, 33, 0, 150, 61, 137, 134, 74, 0, 231, 134, 265, 229, 56, 0, 650, 0, 65, 749, 267, 247, 533, 0, 405, 565
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OFFSET
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1,12
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COMMENTS
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Also strict partitions satisfying (maximum) = 2*(mean).
These are strict partitions where both the diagram and its complement (see example) have size n.
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LINKS
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EXAMPLE
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The a(n) strict partitions for selected n (A..E = 10..14):
n=9: n=12: n=14: n=15: n=16: n=18: n=20: n=21: n=22:
--------------------------------------------------------------
621 831 7421 A32 8431 C42 A532 E43 B542
6321 A41 8521 C51 A541 E52 B632
9432 A631 E61 B641
9531 A721 B731
9621 85421 B821
86321
The a(20) = 6 strict partitions are: (10,7,2,1), (10,6,3,1), (10,5,4,1), (10,5,3,2), (8,6,3,2,1), (8,5,4,2,1).
The strict partition y = (8,5,4,2,1) has diagram:
o o o o o o o o
o o o o o . . .
o o o o . . . .
o o . . . . . .
o . . . . . . .
Since the partition and its complement (shown in dots) have the same size, y is counted under a(20).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[#]*Max@@#==2n&]], {n, 30}]
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CROSSREFS
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A008289 counts strict partitions by length.
A102627 counts strict partitions with integer mean, non-strict A067538.
A116608 counts partitions by number of distinct parts.
Cf. A111907, A237755, A240850, A326849 A359897, A360068, A360071, A360243, A361848, A361851, A361852, A361906.
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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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