A325866 - OEIS

%I #22 Jan 11 2022 08:08:32

%S 1,2,3,6,9,14,20,35,44,76,96,139,179,257,312,483,561,793,970,1459,

%T 1535,2307,2619,3503,4130,5478,5973,8165,9081,11666,13176,17738,18440,

%U 24778,26873,35187,38070,49978,51776,72457,74207,92512,102210,135571,136786,179604

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

%C These are strict knapsack partitions (A275972) organized by maximum rather than sum.

%H Fausto A. C. Cariboni, <a href="/A325866/b325866.txt">Table of n, a(n) for n = 1..150</a>

%e The a(1) = 1 through a(6) = 14 subsets:

%e   {1}  {2}    {3}    {4}      {5}      {6}

%e        {1,2}  {1,3}  {1,4}    {1,5}    {1,6}

%e               {2,3}  {2,4}    {2,5}    {2,6}

%e                      {3,4}    {3,5}    {3,6}

%e                      {1,2,4}  {4,5}    {4,6}

%e                      {2,3,4}  {1,2,5}  {5,6}

%e                               {1,3,5}  {1,2,6}

%e                               {2,4,5}  {1,3,6}

%e                               {3,4,5}  {1,4,6}

%e                                        {2,3,6}

%e                                        {2,5,6}

%e                                        {3,4,6}

%e                                        {3,5,6}

%e                                        {4,5,6}

%t Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&UnsameQ@@Plus@@@Subsets[#]&]],{n,10}]

%Y Cf. A108917, A143823, A143824, A196723, A275972.

%Y Cf. A325860, A325864, A325865, A325867, A325877, A325878, A325880.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jun 01 2019

%E a(18)-a(46) from _Alois P. Heinz_, Jun 03 2019