login
A316402
Number of strict non-knapsack integer partitions of n, meaning not every subset has a different sum.
15
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
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 01 2018
STATUS
approved