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A325857
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Number of integer partitions of n such that every orderless pair of distinct parts has a different sum.
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10
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1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 74, 97, 125, 165, 209, 269, 335, 428, 527, 664, 804, 1005, 1210, 1496, 1780, 2186, 2586, 3148, 3698, 4473, 5226, 6279, 7290, 8706, 10067, 11950, 13744, 16242, 18605, 21864, 24942, 29184, 33188, 38651, 43782, 50791, 57402, 66300, 74683, 86026, 96658
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The A000041(14) - a(14) = 10 partitions of 14 not satisfying the condition are:
(6,5,2,1)
(6,4,3,1)
(5,4,3,2)
(5,4,2,2,1)
(4,4,3,2,1)
(5,4,2,1,1,1)
(4,3,3,2,1,1)
(4,3,2,2,2,1)
(4,3,2,2,1,1,1)
(4,3,2,1,1,1,1,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@Plus@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]
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CROSSREFS
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The integer partition case is A325857.
The strict integer partition case is A325877.
Heinz numbers of the counterexamples are given by A325991.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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