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

Author

Gus Wiseman, Sep 26 2023

Keywords

• nonn

Comments

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

Examples

			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
		

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.

Programs

Mathematica

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