%I #10 Nov 15 2023 08:30:08

%S 1,2,2,6,6,10,17,22,29,42,59,74,102,130,171,226,281,356,454,566,699,

%T 896,1080,1342,1637,2006,2413,2962,3548,4286,5114,6148,7272,8738,

%U 10268,12224,14387,16996,19863,23450,27257,31984,37187,43364,50173,58428,67322

%N Number of subset-sums of strict integer partitions of n.

%C This is the "not necessarily positive" version, cf. A284640.

%e The a(6) = 17 ways, showing each strict partition and its subset-sums:

%e (6): 0,6

%e (51): 0,1,5,6

%e (42): 0,2,4,6

%e (321): 0,1,2,3,4,5,6

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

%Y The positive case is A284640.

%Y The non-strict version is A304792, positive case A276024.

%Y Row sums of A365661, non-strict A365543.

%Y The complement (non-subset-sums) is A365922, non-strict A365918.

%Y A000041 counts integer partitions, strict A000009.

%Y A126796 counts complete partitions, ranks A325781, strict A188431.

%Y A365923 counts partitions by non-subset-sums, strict A365545.

%Y A365924 counts incomplete partitions, ranks A365830, strict A365831.

%Y Cf. A006827, A046663, A364272, A364350, A365658, A365663, A365921.

%K nonn

%O 0,2

%A _Gus Wiseman_, Sep 26 2023