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

0,2

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

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".]

Formula

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

Example

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)

Mathematica

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

Crossrefs

See A007865 for another version.

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

Sequence in context: A364465 A151897 A192758 * A101268 A188920 A281362

Adjacent sequences: A085486 A085487 A085488 * A085490 A085491 A085492

Keyword

nonn,nice

Author

Eric W. Weisstein, Jul 02 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

Status

approved