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A276024 Number of positive subset sums of integer partitions of n. 2
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 February 20 11:03 EST 2018. Contains 299385 sequences. (Running on oeis4.)