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A304792 Number of subset-sums of integer partitions of n. 3
1, 2, 5, 10, 19, 34, 58, 96, 152, 240, 361, 548, 795, 1164, 1647, 2354, 3243, 4534, 6150, 8420, 11240, 15156, 19938, 26514, 34513, 45260, 58298, 75704, 96515, 124064, 157072, 199894, 251097, 317278, 395625, 496184, 615229, 765836, 944045, 1168792, 1432439 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For a multiset p of positive integers summing to n, a pair (t,p) is defined to be a subset sum if there exists a submultiset of p summing to t. This sequence is dominated by A122768 + A000041 (number of submultisets of integer partitions of n).

LINKS

Table of n, a(n) for n=0..40.

FORMULA

a(n) = A276024(n) + A000041(n).

EXAMPLE

The a(4)=19 subset sums are (0,4), (4,4), (0,31), (1,31), (3,31), (4,31), (0,22), (2,22), (4,22), (0,211), (1,211), (2,211), (3,211), (4,211), (0,1111), (1,1111), (2,1111), (3,1111), (4,1111).

MAPLE

b:= proc(n, i, s) option remember; `if`(n=0, nops(s),

     `if`(i<1, 0, b(n, i-1, s)+b(n-i, min(n-i, i),

      map(x-> [x, x+i][], s))))

    end:

a:= n-> b(n$2, {0}):

seq(a(n), n=0..40);  # Alois P. Heinz, May 18 2018

MATHEMATICA

Table[Total[Length[Union[Total/@Subsets[#]]]&/@IntegerPartitions[n]], {n, 15}]

CROSSREFS

Cf. A000041, A108917, A122768, A276024, A284640, A299701, A301856, A301934, A301979, A304793.

Sequence in context: A132210 A000098 A024827 * A104161 A288579 A065613

Adjacent sequences:  A304789 A304790 A304791 * A304793 A304794 A304795

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 18 2018

STATUS

approved

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Last modified March 6 20:37 EST 2021. Contains 341850 sequences. (Running on oeis4.)