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

Author

Gus Wiseman, Jul 01 2018

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

Mathematica

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

Formula

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