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A364755 Number of subsets of {1..n} containing n but not containing the sum of any two distinct elements.

%I A364755 #10 Jan 13 2024 16:46:03
%S A364755 0,1,2,3,6,9,15,24,41,60,99,149,236,355,552,817,1275,1870,2788,4167,
%T A364755 6243,9098,13433,19718,28771,42137,60652,88603,127555,185200,261781,
%U A364755 382931,541022,783862,1096608,1595829,2217467,3223064,4441073,6465800,8893694
%N A364755 Number of subsets of {1..n} containing n but not containing the sum of any two distinct elements.
%H A364755 Andrew Howroyd, <a href="/A364755/b364755.txt">Table of n, a(n) for n = 0..75</a>
%F A364755 First differences of A085489.
%e A364755 The subset S = {1,3,6,8} has pair-sums {4,7,9,11,14}, which are disjoint from S, so it is counted under a(8).
%e A364755 The a(1) = 1 through a(6) = 15 subsets:
%e A364755   {1}  {2}    {3}    {4}      {5}      {6}
%e A364755        {1,2}  {1,3}  {1,4}    {1,5}    {1,6}
%e A364755               {2,3}  {2,4}    {2,5}    {2,6}
%e A364755                      {3,4}    {3,5}    {3,6}
%e A364755                      {1,2,4}  {4,5}    {4,6}
%e A364755                      {2,3,4}  {1,2,5}  {5,6}
%e A364755                               {1,3,5}  {1,2,6}
%e A364755                               {2,4,5}  {1,3,6}
%e A364755                               {3,4,5}  {1,4,6}
%e A364755                                        {2,3,6}
%e A364755                                        {2,5,6}
%e A364755                                        {3,4,6}
%e A364755                                        {3,5,6}
%e A364755                                        {4,5,6}
%e A364755                                        {3,4,5,6}
%t A364755 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&Intersection[#,Total/@Subsets[#,{2}]]=={}&]],{n,0,10}]
%Y A364755 Partial sums are A085489(n) - 1, complement counted by A364534.
%Y A364755 With re-usable parts we have A288728.
%Y A364755 The complement with n is counted by A364756, first differences of A088809.
%Y A364755 Cf. A007865, A050291, A054519, A093971, A151897, A236912, A326020, A326080, A326083, A364272, A364349, A364533.
%K A364755 nonn
%O A364755 0,3
%A A364755 _Gus Wiseman_, Aug 11 2023
%E A364755 a(21) onwards added (using A085489) by _Andrew Howroyd_, Jan 13 2024