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%I #9 Sep 21 2023 12:15:41
%S 0,0,0,2,4,14,28,74,148,350,700,1562,3124,6734,13468,28394,56788,
%T 117950,235900,484922,969844,1979054,3958108,8034314,16068628,
%U 32491550,64983100,131029082,262058164,527304974,1054609948,2118785834,4237571668,8503841150,17007682300
%N Number of subsets of {1..n} containing two distinct elements summing to n.
%F a(n) = 2^n - A068911(n).
%e The a(1) = 0 through a(5) = 14 subsets:
%e . . {1,2} {1,3} {1,4}
%e {1,2,3} {1,2,3} {2,3}
%e {1,3,4} {1,2,3}
%e {1,2,3,4} {1,2,4}
%e {1,3,4}
%e {1,4,5}
%e {2,3,4}
%e {2,3,5}
%e {1,2,3,4}
%e {1,2,3,5}
%e {1,2,4,5}
%e {1,3,4,5}
%e {2,3,4,5}
%e {1,2,3,4,5}
%t Table[Length[Select[Subsets[Range[n]],MemberQ[Total/@Subsets[#,{2}],n]&]],{n,0,10}]
%Y For strict partitions we have A140106 shifted left.
%Y The version for partitions is A004526.
%Y The complement is counted by A068911.
%Y For all subsets of elements we have A365376.
%Y Main diagonal k = n of A365541.
%Y A000009 counts subsets summing to n.
%Y A007865/A085489/A151897 count certain types of sum-free subsets.
%Y A093971/A088809/A364534 count certain types of sum-full subsets.
%Y A365381 counts subsets with a subset summing to k.
%Y Cf. A008967, A095944, A167762, A238628, A288728, A326083, A364272, A365377.
%K nonn
%O 0,4
%A _Gus Wiseman_, Sep 20 2023
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