A316402 - OEIS

%I #4 Jul 01 2018 21:18:31

%S 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,

%T 125,126,180,179,242,247,336,347,444,472,606,628,796,844,1053,1109,

%U 1363,1452,1779,1885,2272,2431,2931,3104,3706,3972,4711,5042,5909,6334

%N Number of strict non-knapsack integer partitions of n, meaning not every subset has a different sum.

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

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

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

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

%K nonn

%O 1,10

%A _Gus Wiseman_, Jul 01 2018