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A276024 Number of positive subset sums of integer partitions of n. 34
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

Table of n, a(n) for n=1..45.

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 October 15 19:24 EDT 2018. Contains 316237 sequences. (Running on oeis4.)