A326174 Number of subsets of {1..n} containing n whose sum is greater than or equal to the sum of their complement.

1, 2, 4, 7, 13, 25, 50, 98, 186, 366, 739, 1457, 2822, 5589, 11258, 22304, 43629, 86658, 174257, 346180, 680955, 1354829, 2721296, 5414787, 10689261, 21290468, 42730228, 85112982, 168430866, 335726276, 673421519, 1342347992, 2661053796, 5307062034, 10640664164

Offset: 1

Author

Gus Wiseman, Jun 11 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(5) = 13 subsets:
  {1}  {2}    {3}      {1,4}      {3,5}
       {1,2}  {1,3}    {2,4}      {4,5}
              {2,3}    {3,4}      {1,2,5}
              {1,2,3}  {1,2,4}    {1,3,5}
                       {1,3,4}    {1,4,5}
                       {2,3,4}    {2,3,5}
                       {1,2,3,4}  {2,4,5}
                                  {3,4,5}
                                  {1,2,3,5}
                                  {1,2,4,5}
                                  {1,3,4,5}
                                  {2,3,4,5}
                                  {1,2,3,4,5}
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 1..46

Crossrefs

Cf. A053632, A057567, A057568, A059529, A063865, A326152, A326173, A326175.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&Plus@@#>=Plus@@Complement[Range[n],#]&]],{n,10}]

Extensions

a(21)-a(42) from Bert Dobbelaere, Jun 22 2019