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A326498 Number of maximal subsets of {1..n} containing no sums of distinct elements. 6
1, 1, 1, 3, 3, 6, 11, 16, 20, 32, 53, 78, 107, 149, 206, 292, 391, 556, 782, 1062, 1451, 1929, 2564, 3404, 4431, 5853, 7672, 9999, 12973, 16922, 22194, 28655, 36734, 47036, 60375, 76866, 97892, 123627, 157008, 196633, 248221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..40.

Andrew Howroyd, PARI Program

EXAMPLE

The a(1) = 1 through a(7) = 16 subsets:

  {1}  {1,2}  {1,2}  {1,3}    {1,2,4}  {1,2,4}    {1,2,4}

              {1,3}  {1,2,4}  {1,2,5}  {1,2,5}    {1,2,5}

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

                              {2,3,4}  {1,3,5}    {1,2,7}

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

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

                                       {2,3,4}    {1,4,7}

                                       {2,3,6}    {2,3,4}

                                       {2,4,5}    {2,4,5}

                                       {2,5,6}    {2,4,7}

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

                                                  {1,3,5,7}

                                                  {2,3,6,7}

                                                  {3,4,5,6}

                                                  {3,5,6,7}

                                                  {4,5,6,7}

MATHEMATICA

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];

Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Plus@@@Subsets[#, {2, n}]]=={}&]]], {n, 0, 10}]

PROG

(PARI) \\ See link for program file.

for(n=0, 25, print1(A326498(n), ", ")) \\ Andrew Howroyd, Aug 29 2019

CROSSREFS

Subsets without sums of distinct elements are A151897.

Maximal sum-free subsets are A121269.

Subsets with sums are A326083.

Maximal subsets without products of distinct elements are A325710.

Maximal subsets without sums or products of distinct elements are A326025.

Cf. A007865, A103580, A326117, A326495, A326497.

Sequence in context: A169944 A110952 A025250 * A094305 A057963 A250301

Adjacent sequences:  A326495 A326496 A326497 * A326499 A326500 A326501

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 09 2019

EXTENSIONS

a(16)-a(40) from Andrew Howroyd, Aug 29 2019

STATUS

approved

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Last modified February 28 01:30 EST 2020. Contains 332319 sequences. (Running on oeis4.)