A284640 Number of positive subset sums of strict integer partitions of n.

1, 1, 4, 4, 7, 13, 17, 23, 34, 49, 62, 87, 112, 149, 199, 249, 318, 408, 512, 635, 820, 991, 1238, 1515, 1864, 2248, 2770, 3326, 4030, 4818, 5808, 6882, 8290, 9756, 11639, 13719, 16236, 18999, 22468, 26144, 30724, 35761, 41754, 48357, 56380, 65018, 75438

Offset: 1

Author

Gus Wiseman, Mar 31 2017

Keywords

• nonn

Comments

For a strict integer partition p summing to n, a pair (t,p) is defined to be a positive subset sum if there exists a nonempty subset of p summing to t.

Examples

			The a(6)=13 subset sums are:
(6,6),
(1,51), (5,51), (6,51),
(2,42), (4,42), (6,42),
(1,321), (2,321), (3,321), (4,321), (5,321), (6,321).
		

Links

• Robert Price, Table of n, a(n) for n = 1..80

Crossrefs

Cf. A122768, A275972, A276024.

Programs

Mathematica

nn=25;Total/@Table[Function[ptn,Length[Union[Total/@Rest[Subsets[ptn]]]]]/@Select[IntegerPartitions[n],UnsameQ@@#&],{n,nn}]