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 A121269 Number of maximal sum-free subsets of {1,2,...,n}. 8
 1, 1, 2, 2, 4, 5, 6, 8, 13, 17, 23, 29, 37, 51, 66, 86, 118, 158, 201, 265, 359, 471, 598, 797, 1043, 1378, 1765, 2311, 3064, 3970, 5017, 6537, 8547, 11020, 14007, 18026, 23404, 30026, 37989, 48945, 62759, 80256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of maximal subsets of {1..n} containing no differences of pairs of elements. - Gus Wiseman, Jul 10 2019 LINKS N. Hindman and H. Jordan, Measures of sum-free intersecting families, New York J. Math. 13 (2007), 97-106. EXAMPLE a(5)=5 because the maximal sum-free subsets of {1,2,3,4,5} are {1,4}, {2,3}, {2,5}, {1,3,5} and {3,4,5} From Gus Wiseman, Jul 10 2019: (Start) The a(1) = 1 through a(8) = 13 subsets:   {1}  {1}  {1,3}  {1,3}  {1,4}    {2,3}    {1,4,6}    {1,3,8}        {2}  {2,3}  {1,4}  {2,3}    {1,3,5}  {1,4,7}    {1,4,6}                    {2,3}  {2,5}    {1,4,6}  {2,3,7}    {1,4,7}                    {3,4}  {1,3,5}  {2,5,6}  {2,5,6}    {1,5,8}                           {3,4,5}  {3,4,5}  {2,6,7}    {1,6,8}                                    {4,5,6}  {3,4,5}    {2,5,6}                                             {1,3,5,7}  {2,5,8}                                             {4,5,6,7}  {2,6,7}                                                        {3,4,5}                                                        {1,3,5,7}                                                        {2,3,7,8}                                                        {4,5,6,7}                                                        {5,6,7,8} (End) MATHEMATICA fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)]; Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Plus@@@Tuples[#, 2]]=={}&]]], {n, 0, 10}] (* Gus Wiseman, Jul 10 2019 *) CROSSREFS Maximal product-free subsets are A326496. Sum-free subsets are A007865. Maximal sum-free and product-free subsets are A326497. Subsets with sums are A326083. Maximal subsets without sums of distinct elements are A326498. Cf. A103580, A326020, A326489, A326495. Sequence in context: A238687 A238433 A238424 * A211860 A250114 A056219 Adjacent sequences:  A121266 A121267 A121268 * A121270 A121271 A121272 KEYWORD nonn AUTHOR N. Hindman (nhindman(AT)aol.com), Aug 23 2006 EXTENSIONS a(0) = 1 prepended by Gus Wiseman, Jul 10 2019 STATUS approved

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)