A316401 Number of strict integer partitions of n that are not knapsack (not every subset has a different sum) but every subset has a different average.

0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 3, 1, 3, 2, 4, 2, 6, 6, 11, 9, 9, 10, 20, 16, 18, 17, 27, 24, 31, 29, 43, 31, 43, 40, 59, 52, 58, 61, 83, 68, 93, 80, 124, 99, 120, 109, 145, 151, 185, 160, 232, 163, 257, 229, 314, 280, 286, 310, 427, 385, 513, 333, 596

Offset

1,10

Links

Table of n, a(n) for n=1..66.

Example

The a(22) = 11 partitions:
(11,6,5), (11,7,4), (11,8,3), (11,9,2), (11,10,1),
(11,5,4,2), (11,6,3,2), (11,8,2,1), (12,5,3,2), (12,5,4,1), (14,4,3,1).

Mathematica

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

Crossrefs

Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316313, A316314, A316399, A316400.

Sequence in context: A125989 A125924 A283929 * A082513 A187495 A187496

Adjacent sequences: A316398 A316399 A316400 * A316402 A316403 A316404

Keyword

nonn

Author

Gus Wiseman, Jul 01 2018

Status

approved