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A304796 Number of special sums of integer partitions of n.

%I A304796 #13 Sep 26 2023 14:58:01
%S A304796 1,2,5,10,18,32,51,82,122,188,262,392,529,750,997,1404,1784,2452,3123,
%T A304796 4164,5239,6916,8499,11112,13693,17482,21257,27162,32581,41114,49606,
%U A304796 61418,73474,91086,107780,132874,157359,191026,225159,274110,320691,386722,453875
%N A304796 Number of special sums of integer partitions of n.
%C A304796 A special sum of an integer partition y is a number n >= 0 such that exactly one submultiset of y sums to n.
%F A304796 a(n) = A301854(n) + A000041(n).
%e A304796 The a(4) = 18 special positive subset-sums:
%e A304796 0<=(4), 4<=(4),
%e A304796 0<=(22), 2<=(22), 4<=(22),
%e A304796 0<=(31), 1<=(31), 3<=(31), 4<=(31),
%e A304796 0<=(211), 1<=(211), 3<=(211), 4<=(211),
%e A304796 0<=(1111), 1<=(1111), 2<=(1111), 3<=(1111), 4<=(1111).
%t A304796 uqsubs[y_]:=Join@@Select[GatherBy[Union[Subsets[y]],Total],Length[#]===1&];
%t A304796 Table[Total[Length/@uqsubs/@IntegerPartitions[n]],{n,25}]
%Y A304796 Cf. A000712, A108917, A122768, A275972, A276024, A284640, A299701, A299702, A299729, A301829, A301830, A301854.
%K A304796 nonn
%O A304796 0,2
%A A304796 _Gus Wiseman_, May 18 2018
%E A304796 More terms from _Alois P. Heinz_, May 18 2018
%E A304796 a(36)-a(42) from _Chai Wah Wu_, Sep 26 2023