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

1,3

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.

Links

Table of n, a(n) for n=1..47.

Example

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).

Mathematica

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

Crossrefs

Cf. A122768, A275972, A276024.

Sequence in context: A357270 A347060 A211643 * A036605 A183541 A323657

Adjacent sequences: A284637 A284638 A284639 * A284641 A284642 A284643

Keyword

nonn

Author

Gus Wiseman, Mar 31 2017

Status

approved