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 A276024 Number of positive subset sums of integer partitions of n. 42
 1, 3, 7, 14, 27, 47, 81, 130, 210, 319, 492, 718, 1063, 1512, 2178, 3012, 4237, 5765, 7930, 10613, 14364, 18936, 25259, 32938, 43302, 55862, 72694, 92797, 119499, 151468, 193052, 242748, 307135, 383315, 481301, 597252, 744199, 918030, 1137607, 1395101, 1718237, 2098096, 2569047, 3121825, 3805722 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For a multiset p of positive integers summing to n, a pair (t,p) is defined to be a positive subset sum if there exists a nonempty submultiset of p summing to t. Positive integers with positive subset sums form a multiorder. This sequence is dominated by A122768 (submultisets of integer partitions of n). LINKS Konstantinos Koiliaris and Chao Xu, A Faster Pseudopolynomial Time Algorithm for Subset Sum, arXiv:1507.02318 [cs.DS], 2015-2016. Gus Wiseman, Comcategories and Multiorders (pdf version) EXAMPLE The a(4)=14 positive subset sums are: {(4,4), (1,31), (3,31), (4,31), (2,22), (4,22), (1,211), (2,211), (3,211), (4,211), (1,1111), (2,1111), (3,1111), (4,1111)}. MATHEMATICA sums[ptn_?OrderedQ]:=sums[ptn]=If[Length[ptn]===1, ptn, Module[{pri, sms}, pri=Union[Table[Delete[ptn, i], {i, Length[ptn]}]]; sms=Join[sums[#], sums[#]+Total[ptn]-Total[#]]&/@pri; Union@@sms ]]; Table[Total[Length[sums[Sort[#]]]&/@IntegerPartitions[n]], {n, 1, 25}] CROSSREFS Cf. A122768, A063834, A262671. Sequence in context: A245268 A117071 A019459 * A274233 A256209 A236914 Adjacent sequences:  A276021 A276022 A276023 * A276025 A276026 A276027 KEYWORD nonn AUTHOR Gus Wiseman, Aug 16 2016 STATUS approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)