A364755 Number of subsets of {1..n} containing n but not containing the sum of any two distinct elements.

0, 1, 2, 3, 6, 9, 15, 24, 41, 60, 99, 149, 236, 355, 552, 817, 1275, 1870, 2788, 4167, 6243, 9098, 13433, 19718, 28771, 42137, 60652, 88603, 127555, 185200, 261781, 382931, 541022, 783862, 1096608, 1595829, 2217467, 3223064, 4441073, 6465800, 8893694

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..75

Formula

First differences of A085489.

Example

The subset S = {1,3,6,8} has pair-sums {4,7,9,11,14}, which are disjoint from S, so it is counted under a(8).
The a(1) = 1 through a(6) = 15 subsets:
  {1}  {2}    {3}    {4}      {5}      {6}
       {1,2}  {1,3}  {1,4}    {1,5}    {1,6}
              {2,3}  {2,4}    {2,5}    {2,6}
                     {3,4}    {3,5}    {3,6}
                     {1,2,4}  {4,5}    {4,6}
                     {2,3,4}  {1,2,5}  {5,6}
                              {1,3,5}  {1,2,6}
                              {2,4,5}  {1,3,6}
                              {3,4,5}  {1,4,6}
                                       {2,3,6}
                                       {2,5,6}
                                       {3,4,6}
                                       {3,5,6}
                                       {4,5,6}
                                       {3,4,5,6}

Mathematica

Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Intersection[#, Total/@Subsets[#, {2}]]=={}&]], {n, 0, 10}]

Crossrefs

Partial sums are A085489(n) - 1, complement counted by A364534.

With re-usable parts we have A288728.

The complement with n is counted by A364756, first differences of A088809.

Cf. A007865, A050291, A054519, A093971, A151897, A236912, A326020, A326080, A326083, A364272, A364349, A364533.

Sequence in context: A365071 A192671 A080239 * A114323 A355324 A293631

Adjacent sequences: A364752 A364753 A364754 * A364756 A364757 A364758

Keyword

nonn

Author

Gus Wiseman, Aug 11 2023

Extensions

a(21) onwards added (using A085489) by Andrew Howroyd, Jan 13 2024

Status

approved