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A366738
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Number of semi-sums of integer partitions of n.
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21
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0, 0, 1, 2, 5, 9, 17, 28, 46, 72, 111, 166, 243, 352, 500, 704, 973, 1341, 1819, 2459, 3277, 4363, 5735, 7529, 9779, 12685, 16301, 20929, 26638, 33878, 42778, 53942, 67583, 84600, 105270, 130853, 161835, 199896, 245788, 301890, 369208, 451046, 549002, 667370
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OFFSET
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0,4
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COMMENTS
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We define a semi-sum of a multiset to be any sum of a 2-element submultiset. This is different from sums of pairs of elements. For example, 2 is the sum of a pair of elements of {1}, but there are no semi-sums.
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LINKS
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EXAMPLE
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The partitions of 6 and their a(6) = 17 semi-sums:
(6) ->
(51) -> 6
(42) -> 6
(411) -> 2,5
(33) -> 6
(321) -> 3,4,5
(3111) -> 2,4
(222) -> 4
(2211) -> 2,3,4
(21111) -> 2,3
(111111) -> 2
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MATHEMATICA
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Table[Total[Length[Union[Total/@Subsets[#, {2}]]]&/@IntegerPartitions[n]], {n, 0, 15}]
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CROSSREFS
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The strict non-binary version is A365925.
For prime indices instead of partitions we have A366739.
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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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