A316400 - OEIS

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

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OFFSET

1,9

LINKS

Table of n, a(n) for n=1..64.

EXAMPLE

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).

MATHEMATICA

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

CROSSREFS