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A366754
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Number of non-knapsack integer partitions of n.
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14
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0, 0, 0, 0, 1, 1, 4, 4, 10, 13, 23, 27, 52, 60, 94, 118, 175, 213, 310, 373, 528, 643, 862, 1044, 1403, 1699, 2199, 2676, 3426, 4131, 5256, 6295, 7884, 9479, 11722, 14047, 17296, 20623, 25142, 29942, 36299, 43081, 51950, 61439, 73668, 87040, 103748, 122149, 145155, 170487
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OFFSET
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0,7
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COMMENTS
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A multiset is non-knapsack if there exist two different submultisets with the same sum.
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 1 through a(9) = 13 partitions:
(211) (2111) (321) (3211) (422) (3321)
(2211) (22111) (431) (4221)
(3111) (31111) (3221) (4311)
(21111) (211111) (4211) (5211)
(22211) (32211)
(32111) (33111)
(41111) (42111)
(221111) (222111)
(311111) (321111)
(2111111) (411111)
(2211111)
(3111111)
(21111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Total/@Union[Subsets[#]]&]], {n, 0, 15}]
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CROSSREFS
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These partitions have ranks A299729.
A365661 counts strict partitions with subset-sum k, complement A365663.
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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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