A365925 Number of subset-sums of strict integer partitions of n.

1, 2, 2, 6, 6, 10, 17, 22, 29, 42, 59, 74, 102, 130, 171, 226, 281, 356, 454, 566, 699, 896, 1080, 1342, 1637, 2006, 2413, 2962, 3548, 4286, 5114, 6148, 7272, 8738, 10268, 12224, 14387, 16996, 19863, 23450, 27257, 31984, 37187, 43364, 50173, 58428, 67322

Offset

0,2

Comments

This is the "not necessarily positive" version, cf. A284640.

Links

Table of n, a(n) for n=0..46.

Example

The a(6) = 17 ways, showing each strict partition and its subset-sums:
    (6): 0,6
   (51): 0,1,5,6
   (42): 0,2,4,6
  (321): 0,1,2,3,4,5,6

Mathematica

Table[Total[Length[Union[Total/@Subsets[#]]]& /@ Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 30}]

Crossrefs

The positive case is A284640.

The non-strict version is A304792, positive case A276024.

Row sums of A365661, non-strict A365543.

The complement (non-subset-sums) is A365922, non-strict A365918.

A000041 counts integer partitions, strict A000009.

A126796 counts complete partitions, ranks A325781, strict A188431.

A365923 counts partitions by non-subset-sums, strict A365545.

A365924 counts incomplete partitions, ranks A365830, strict A365831.

Cf. A006827, A046663, A364272, A364350, A365658, A365663, A365921.

Sequence in context: A237363 A082542 A162776 * A032302 A032214 A290261

Adjacent sequences: A365922 A365923 A365924 * A365926 A365927 A365928

Keyword

nonn

Author

Gus Wiseman, Sep 26 2023

Status

approved