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A316401
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Number of strict integer partitions of n that are not knapsack (not every subset has a different sum) but every subset has a different average.
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1
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0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 3, 1, 3, 2, 4, 2, 6, 6, 11, 9, 9, 10, 20, 16, 18, 17, 27, 24, 31, 29, 43, 31, 43, 40, 59, 52, 58, 61, 83, 68, 93, 80, 124, 99, 120, 109, 145, 151, 185, 160, 232, 163, 257, 229, 314, 280, 286, 310, 427, 385, 513, 333, 596
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OFFSET
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1,10
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LINKS
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EXAMPLE
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The a(22) = 11 partitions:
(11,6,5), (11,7,4), (11,8,3), (11,9,2), (11,10,1),
(11,5,4,2), (11,6,3,2), (11,8,2,1), (12,5,3,2), (12,5,4,1), (14,4,3,1).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!UnsameQ@@Total/@Union[Subsets[#]]&&UnsameQ@@Mean/@Union[Subsets[#]]&]], {n, 20}]
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CROSSREFS
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Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316313, A316314, A316399, A316400.
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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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