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A325862
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Number of integer partitions of n such that every set of distinct parts has a different sum.
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30
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1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 34, 46, 58, 77, 93, 122, 146, 188, 217, 282, 327, 410, 470, 596, 673, 848, 947, 1178, 1325, 1629, 1798, 2213, 2444, 2962, 3247, 3935, 4292, 5149, 5579, 6674, 7247, 8590, 9221, 10964, 11804, 13870, 14843, 17480, 18675, 21866
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OFFSET
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0,3
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COMMENTS
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A knapsack partition (A108917, A299702) is an integer partition such that every submultiset has a different sum. The one non-knapsack partition counted under a(4) is (2,1,1).
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LINKS
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EXAMPLE
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The a(1) = 1 through a(7) = 14 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (411) (331)
(11111) (2211) (421)
(3111) (511)
(21111) (2221)
(111111) (4111)
(22111)
(31111)
(211111)
(1111111)
The three non-knapsack partitions counted under a(6) are:
(2,2,1,1)
(3,1,1,1)
(2,1,1,1,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@Plus@@@Subsets[Union[#]]&]], {n, 0, 20}]
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CROSSREFS
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Cf. A002033, A034444, A196723, A275972, A276024, A299702, A325592, A325856, A325863, A325864, A325865, A325877.
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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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