A364756 Number of subsets of {1..n} containing n and some element equal to the sum of two distinct others.

0, 0, 0, 1, 2, 7, 17, 40, 87, 196, 413, 875, 1812, 3741, 7640, 15567, 31493, 63666, 128284, 257977, 518045, 1039478, 2083719, 4174586, 8359837, 16735079, 33493780, 67020261, 134090173, 268250256, 536609131, 1073358893, 2146942626, 4294183434, 8588837984, 17178273355

Offset

0,5

Links

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

Formula

First differences of A088809.

Example

The subset S = {1,3,6,8} has pair-sums {4,7,9,11,14}, which are disjoint from S, so it is not counted under a(8).
The subset {2,3,4,6} has pair-sum 2 + 4 = 6, so is counted under a(6).
The a(0) = 0 through a(6) = 17 subsets:
  .  .  .  {1,2,3}  {1,3,4}    {1,4,5}      {1,5,6}
                    {1,2,3,4}  {2,3,5}      {2,4,6}
                               {1,2,3,5}    {1,2,3,6}
                               {1,2,4,5}    {1,2,4,6}
                               {1,3,4,5}    {1,2,5,6}
                               {2,3,4,5}    {1,3,4,6}
                               {1,2,3,4,5}  {1,3,5,6}
                                            {1,4,5,6}
                                            {2,3,4,6}
                                            {2,3,5,6}
                                            {2,4,5,6}
                                            {1,2,3,4,6}
                                            {1,2,3,5,6}
                                            {1,2,4,5,6}
                                            {1,3,4,5,6}
                                            {2,3,4,5,6}
                                            {1,2,3,4,5,6}

Mathematica

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

Crossrefs

Partial sums are A088809, non-binary A364534.

With re-usable parts we have differences of A093971, complement A288728.

The complement with n is counted by A364755, partial sums A085489(n) - 1.

Cf. A000079, A007865, A050291, A051026, A103580, A151897, A236912, A326080, A326083, A364272.

Sequence in context: A173769 A067038 A209398 * A175660 A365069 A347079

Adjacent sequences: A364753 A364754 A364755 * A364757 A364758 A364759

Keyword

nonn

Author

Gus Wiseman, Aug 11 2023

Extensions

a(16) onwards added (using A088809) by Andrew Howroyd, Jan 13 2024

Status

approved