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A304796 Number of special sums of integer partitions of n. 2
1, 2, 5, 10, 18, 32, 51, 82, 122, 188, 262, 392, 529, 750, 997, 1404, 1784, 2452, 3123, 4164, 5239, 6916, 8499, 11112, 13693, 17482, 21257, 27162, 32581, 41114, 49606, 61418, 73474, 91086, 107780, 132874 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A 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=0..35.

FORMULA

a(n) = A301854(n) + A000041(n).

EXAMPLE

The a(4) = 18 special positive subset-sums:

0<=(4), 4<=(4),

0<=(22), 2<=(22), 4<=(22),

0<=(31), 1<=(31), 3<=(31), 4<=(31),

0<=(211), 1<=(211), 3<=(211), 4<=(211),

0<=(1111), 1<=(1111), 2<=(1111), 3<=(1111), 4<=(1111).

MATHEMATICA

uqsubs[y_]:=Join@@Select[GatherBy[Union[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.

Sequence in context: A034350 A006327 A185721 * A103577 A326508 A079006

Adjacent sequences:  A304793 A304794 A304795 * A304797 A304798 A304799

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 18 2018

EXTENSIONS

More terms from Alois P. Heinz, May 18 2018

STATUS

approved

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Last modified July 23 11:34 EDT 2021. Contains 346259 sequences. (Running on oeis4.)