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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

Table of n, a(n) for n=0..41.

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.)