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 A325867 Number of maximal subsets of {1...n} containing n such that every subset has a different sum. 9
 1, 1, 2, 2, 4, 8, 10, 12, 17, 34, 45, 77, 99, 136, 166, 200, 238, 328, 402, 660, 674, 1166, 1331, 1966, 2335, 3286, 3527, 4762, 5383, 6900, 7543, 9087, 10149, 12239, 13569, 16452, 17867, 22869, 23977, 33881, 33820, 43423, 48090, 68683, 67347, 95176, 97917, 131666, 136205 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS These are maximal strict knapsack partitions (A275972, A326015) organized by maximum rather than sum. LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..121 EXAMPLE The a(1) = 1 through a(8) = 12 subsets:   {1}  {1,2}  {1,3}  {1,2,4}  {1,2,5}  {1,2,6}  {1,2,7}    {1,3,8}               {2,3}  {2,3,4}  {1,3,5}  {1,3,6}  {1,3,7}    {1,5,8}                               {2,4,5}  {1,4,6}  {1,4,7}    {5,7,8}                               {3,4,5}  {2,3,6}  {1,5,7}    {1,2,4,8}                                        {2,5,6}  {2,3,7}    {1,4,6,8}                                        {3,4,6}  {2,4,7}    {2,3,4,8}                                        {3,5,6}  {2,6,7}    {2,4,5,8}                                        {4,5,6}  {4,5,7}    {2,4,7,8}                                                 {4,6,7}    {3,4,6,8}                                                 {3,5,6,7}  {3,6,7,8}                                                            {4,5,6,8}                                                            {4,6,7,8} MATHEMATICA fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&)/@y]; Table[Length[fasmax[Select[Subsets[Range[n]], MemberQ[#, n]&&UnsameQ@@Plus@@@Subsets[#]&]]], {n, 15}] PROG (Python) def f(p0, n, m, cm):     full, t, p = True, 0, p0     while p>k)&1)==0 and ((m<

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)