This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316402 #4 Jul 01 2018 21:18:31
%S A316402 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 A316402 125,126,180,179,242,247,336,347,444,472,606,628,796,844,1053,1109,
%U A316402 1363,1452,1779,1885,2272,2431,2931,3104,3706,3972,4711,5042,5909,6334
%N A316402 Number of strict non-knapsack integer partitions of n, meaning not every subset has a different sum.
%F A316402 a(n) = A000009(n) - A275972(n).
%e A316402 The a(12) = 4 partitions are (6,4,2), (6,5,1), (5,4,2,1), (6,3,2,1).
%t A316402 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!UnsameQ@@Total/@Union[Subsets[#]]&]],{n,30}]
%Y A316402 Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316314, A316399, A316400.
%K A316402 nonn
%O A316402 1,10
%A A316402 _Gus Wiseman_, Jul 01 2018