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A284640 Number of positive subset sums of strict integer partitions of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A293678 A063984 A211643 * A036605 A183541 A238389

Adjacent sequences:  A284637 A284638 A284639 * A284641 A284642 A284643

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 31 2017

STATUS

approved

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Last modified February 22 18:16 EST 2018. Contains 299469 sequences. (Running on oeis4.)