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A364756 Number of subsets of {1..n} containing n and some element equal to the sum of two distinct others.

%I A364756 #10 Jan 13 2024 16:46:38
%S A364756 0,0,0,1,2,7,17,40,87,196,413,875,1812,3741,7640,15567,31493,63666,
%T A364756 128284,257977,518045,1039478,2083719,4174586,8359837,16735079,
%U A364756 33493780,67020261,134090173,268250256,536609131,1073358893,2146942626,4294183434,8588837984,17178273355
%N A364756 Number of subsets of {1..n} containing n and some element equal to the sum of two distinct others.
%H A364756 Andrew Howroyd, <a href="/A364756/b364756.txt">Table of n, a(n) for n = 0..75</a>
%F A364756 First differences of A088809.
%e A364756 The subset S = {1,3,6,8} has pair-sums {4,7,9,11,14}, which are disjoint from S, so it is not counted under a(8).
%e A364756 The subset {2,3,4,6} has pair-sum 2 + 4 = 6, so is counted under a(6).
%e A364756 The a(0) = 0 through a(6) = 17 subsets:
%e A364756   .  .  .  {1,2,3}  {1,3,4}    {1,4,5}      {1,5,6}
%e A364756                     {1,2,3,4}  {2,3,5}      {2,4,6}
%e A364756                                {1,2,3,5}    {1,2,3,6}
%e A364756                                {1,2,4,5}    {1,2,4,6}
%e A364756                                {1,3,4,5}    {1,2,5,6}
%e A364756                                {2,3,4,5}    {1,3,4,6}
%e A364756                                {1,2,3,4,5}  {1,3,5,6}
%e A364756                                             {1,4,5,6}
%e A364756                                             {2,3,4,6}
%e A364756                                             {2,3,5,6}
%e A364756                                             {2,4,5,6}
%e A364756                                             {1,2,3,4,6}
%e A364756                                             {1,2,3,5,6}
%e A364756                                             {1,2,4,5,6}
%e A364756                                             {1,3,4,5,6}
%e A364756                                             {2,3,4,5,6}
%e A364756                                             {1,2,3,4,5,6}
%t A364756 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&Intersection[#,Total/@Subsets[#,{2}]]!={}&]],{n,0,10}]
%Y A364756 Partial sums are A088809, non-binary A364534.
%Y A364756 With re-usable parts we have differences of A093971, complement A288728.
%Y A364756 The complement with n is counted by A364755, partial sums A085489(n) - 1.
%Y A364756 Cf. A000079, A007865, A050291, A051026, A103580, A151897, A236912, A326080, A326083, A364272.
%K A364756 nonn
%O A364756 0,5
%A A364756 _Gus Wiseman_, Aug 11 2023
%E A364756 a(16) onwards added (using A088809) by _Andrew Howroyd_, Jan 13 2024