A365922 Number of non-subset-sums of strict integer partitions of n.

0, 1, 2, 4, 8, 11, 18, 25, 38, 51, 70, 93, 122, 159, 206, 263, 328, 420, 514, 645, 776, 967, 1154, 1413, 1686, 2042, 2414, 2890, 3394, 4062, 4732, 5598, 6494, 7652, 8836, 10329, 11884, 13833, 15830, 18376, 20936, 24131, 27476, 31547, 35780, 40966, 46292, 52737

Offset

1,3

Comments

For an integer partition y of n, we call a positive integer k <= n a non-subset-sum iff there is no submultiset of y summing to k.

Links

Table of n, a(n) for n=1..48.

Example

The a(6) = 11 ways, showing each strict partition and its non-subset-sums:
    (6): 1,2,3,4,5
   (51): 2,3,4
   (42): 1,3,5
  (321):

Mathematica

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

Crossrefs

The complement (positive subset-sums) is A284640, non-strict A276024.

Weighted row sums of A365545, non-strict A365923.

Row sums of A365663, non-strict A046663.

The non-strict version is A365918.

The zero-full complement (subset-sums) is A365925, non-strict A304792.

A000041 counts integer partitions, strict A000009.

A126796 counts complete partitions, ranks A325781, strict A188431.

A364350 counts combination-free strict partitions, complement A364839.

A365543 counts partitions with a submultiset summing to k.

A365661 counts strict partitions w/ a subset summing to k.

A365924 counts incomplete partitions, ranks A365830, strict A365831.

Cf. A006827, A325799, A364272, A365658, A365919, A365921.

Sequence in context: A007295 A053439 A337501 * A373080 A180379 A033956

Adjacent sequences: A365919 A365920 A365921 * A365923 A365924 A365925

Keyword

nonn

Author

Gus Wiseman, Sep 23 2023

Status

approved