A316402 Number of strict non-knapsack integer partitions of n, meaning not every subset has a different sum.

0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 1, 4, 3, 8, 6, 12, 10, 20, 16, 29, 25, 44, 39, 61, 60, 91, 84, 125, 126, 180, 179, 242, 247, 336, 347, 444, 472, 606, 628, 796, 844, 1053, 1109, 1363, 1452, 1779, 1885, 2272, 2431, 2931, 3104, 3706, 3972, 4711, 5042, 5909, 6334

Offset

1,10

Links

Table of n, a(n) for n=1..57.

Formula

a(n) = A000009(n) - A275972(n).

Example

The a(12) = 4 partitions are (6,4,2), (6,5,1), (5,4,2,1), (6,3,2,1).

Mathematica

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

Crossrefs

Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316314, A316399, A316400.

Sequence in context: A298254 A337588 A364272 * A054907 A245539 A089554

Adjacent sequences: A316399 A316400 A316401 * A316403 A316404 A316405

Keyword

nonn

Author

Gus Wiseman, Jul 01 2018

Status

approved