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A325866 Number of subsets of {1..n} containing n such that every subset has a different sum.

%I A325866 #22 Jan 11 2022 08:08:32
%S A325866 1,2,3,6,9,14,20,35,44,76,96,139,179,257,312,483,561,793,970,1459,
%T A325866 1535,2307,2619,3503,4130,5478,5973,8165,9081,11666,13176,17738,18440,
%U A325866 24778,26873,35187,38070,49978,51776,72457,74207,92512,102210,135571,136786,179604
%N A325866 Number of subsets of {1..n} containing n such that every subset has a different sum.
%C A325866 These are strict knapsack partitions (A275972) organized by maximum rather than sum.
%H A325866 Fausto A. C. Cariboni, <a href="/A325866/b325866.txt">Table of n, a(n) for n = 1..150</a>
%e A325866 The a(1) = 1 through a(6) = 14 subsets:
%e A325866   {1}  {2}    {3}    {4}      {5}      {6}
%e A325866        {1,2}  {1,3}  {1,4}    {1,5}    {1,6}
%e A325866               {2,3}  {2,4}    {2,5}    {2,6}
%e A325866                      {3,4}    {3,5}    {3,6}
%e A325866                      {1,2,4}  {4,5}    {4,6}
%e A325866                      {2,3,4}  {1,2,5}  {5,6}
%e A325866                               {1,3,5}  {1,2,6}
%e A325866                               {2,4,5}  {1,3,6}
%e A325866                               {3,4,5}  {1,4,6}
%e A325866                                        {2,3,6}
%e A325866                                        {2,5,6}
%e A325866                                        {3,4,6}
%e A325866                                        {3,5,6}
%e A325866                                        {4,5,6}
%t A325866 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&UnsameQ@@Plus@@@Subsets[#]&]],{n,10}]
%Y A325866 Cf. A108917, A143823, A143824, A196723, A275972.
%Y A325866 Cf. A325860, A325864, A325865, A325867, A325877, A325878, A325880.
%K A325866 nonn
%O A325866 1,2
%A A325866 _Gus Wiseman_, Jun 01 2019
%E A325866 a(18)-a(46) from _Alois P. Heinz_, Jun 03 2019