A326498 Number of maximal subsets of {1..n} containing no sums of distinct elements.

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, 311442, 390859, 488327, 610685

Offset

0,4

Links

Table of n, a(n) for n=0..44.

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: A110952 A339539 A025250 * A367644 A094305 A360850

Adjacent sequences: A326495 A326496 A326497 * A326499 A326500 A326501

Keyword

nonn

Author

Gus Wiseman, Jul 09 2019

Extensions

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

a(41)-a(44) from Jinyuan Wang, Oct 11 2020

Status

approved