A085489 a(n) is the number of subsets of {1,...,n} containing no solutions to x+y=z with x and y distinct (one version of "sum-free subsets").

1, 2, 4, 7, 13, 22, 37, 61, 102, 162, 261, 410, 646, 1001, 1553, 2370, 3645, 5515, 8303, 12470, 18713, 27811, 41244, 60962, 89733, 131870, 192522, 281125, 408680, 593880, 855661, 1238592, 1779614, 2563476, 3660084, 5255913, 7473380, 10696444, 15137517

Offset: 0

Author

Eric W. Weisstein, Jul 02 2003

Keywords

• nonn
• nice

Comments

First differs from A151897 at a(7) = 61, A151897(7) = 60. The one subset counted under a(7) but not under A151897(7) is {1,2,4,7}. - Gus Wiseman, Jun 07 2019

Examples

			From _Gus Wiseman_, Jun 07 2019: (Start)
The a(0) = 1 through a(4) = 13 subsets:
  {}  {}   {}     {}     {}
      {1}  {1}    {1}    {1}
           {2}    {2}    {2}
           {1,2}  {3}    {3}
                  {1,2}  {4}
                  {1,3}  {1,2}
                  {2,3}  {1,3}
                         {1,4}
                         {2,3}
                         {2,4}
                         {3,4}
                         {1,2,4}
                         {2,3,4}
The a(5) = 22 subsets:
  {}  {1}  {1,2}  {1,2,4}
      {2}  {1,3}  {1,2,5}
      {3}  {1,4}  {1,3,5}
      {4}  {1,5}  {2,3,4}
      {5}  {2,3}  {2,4,5}
           {2,4}  {3,4,5}
           {2,5}
           {3,4}
           {3,5}
           {4,5}
(End)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..75, (terms up to a(57) from Ben Burns)
• Eric Weisstein's World of Mathematics, Sum-Free Set [Strictly speaking this link is not relevant, since it uses a different definition of "sum-free".]

Crossrefs

See A007865 for another version.

Cf. A050291, A051026, A103580, A151897, A308546, A326080, A326083, A326117.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]],Intersection[ #,Select[ Plus@@@ Subsets[ #,{2}],#<=n&]]=={}&]],{n,0,10}] (* Gus Wiseman, Jun 07 2019 *)

Formula

a(n) = 2^n - A088809(n). - Reinhard Zumkeller, Oct 19 2003

Extensions

More terms from Reinhard Zumkeller, Jul 13 2003

Edited by David Wasserman, Apr 16 2008

a(0) = 1 prepended by Gus Wiseman, Jun 07 2019