A316400 Number of strict integer partitions of n that are knapsack (every subset has a different sum) but not every subset has a different average.

0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 1, 2, 4, 6, 4, 13, 6, 13, 17, 15, 12, 31, 26, 27, 23, 36, 41, 56, 39, 47, 74, 71, 55, 101, 94, 110, 97, 145, 148, 189, 142, 214, 232, 280, 206, 362, 332, 414, 347, 504, 469, 658, 492, 726, 697, 867, 687, 1100, 933

Offset: 1

Author

Gus Wiseman, Jul 01 2018

Keywords

• nonn

Examples

			The a(21) = 13 partitions:
(8,7,6), (9,7,5), (10,7,4), (11,7,3), (12,7,2), (13,7,1),
(7,6,5,3), (8,6,4,3), (9,7,4,1), (10,6,3,2), (11,6,3,1), (12,4,3,2), (12,5,3,1).
		

Crossrefs

Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316313, A316314, A316399, A316401.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Total/@Union[Subsets[#]]&&!UnsameQ@@Mean/@Union[Subsets[#]]&]],{n,20}]