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A301854 Number of positive special sums of integer partitions of n. 13
1, 3, 7, 13, 25, 40, 67, 100, 158, 220, 336, 452, 649, 862, 1228, 1553, 2155, 2738, 3674, 4612, 6124, 7497, 9857, 12118, 15524, 18821, 24152, 28863, 36549, 44002, 54576, 65125, 80943, 95470, 117991 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A positive special sum of an integer partition y is a number n > 0 such that exactly one submultiset of y sums to n.

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

The a(4) = 13 special positive subset-sums:

1<=(1111), 2<=(1111), 3<=(1111), 4<=(1111),

1<=(211),  3<=(211),  4<=(211),

1<=(31),   3<=(31),   4<=(31),

2<=(22),   4<=(22),

4<=(4).

MATHEMATICA

uqsubs[y_]:=Join@@Select[GatherBy[Union[Rest[Subsets[y]]], Total], Length[#]===1&];

Table[Total[Length/@uqsubs/@IntegerPartitions[n]], {n, 25}]

CROSSREFS

Cf. A000712, A108917, A122768, A275972, A276024, A284640, A299701, A299702, A299729, A301829, A301830, A301854, A301855, A301856.

Sequence in context: A056764 A026103 A328652 * A092463 A259343 A210613

Adjacent sequences:  A301851 A301852 A301853 * A301855 A301856 A301857

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 27 2018

EXTENSIONS

a(21)-a(35) from Alois P. Heinz, Apr 08 2018

STATUS

approved

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)