A151897 Number of subsets of {1, 2, ..., n} such that no member is a sum of distinct other members.

1, 2, 4, 7, 13, 22, 37, 60, 100, 155, 249, 381, 591, 889, 1365, 2009, 3047, 4453, 6602, 9567, 14151, 20228, 29654, 42302, 61369, 87108, 126066, 177580, 256039, 360304, 515740, 724069, 1036860, 1448746, 2069526, 2893311, 4117725, 5749540, 8186555

Offset

0,2

Comments

This sequence and A085489 first differ at n = 7. a(7) = 60, A085489(7) = 61. A085489(7) includes {1, 2, 4, 7}, which is excluded from a(7) because 1+2+4 = 7.

If this sequence counts sum-free sets, A326080 counts sum-closed sets, which are different from sum-full sets (A093971). - Gus Wiseman, Jun 07 2019

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..85

Example

a(4) = 13, including all subsets of {1, 2, 3, 4} except {1, 2, 3} (excluded
because 1+2 = 3), {1, 3, 4} (excluded because 1+3 = 4), and {1, 2, 3, 4} (excluded for both reasons.)
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}
(End)

Mathematica

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

Crossrefs

Cf. A007865, A050291, A085489, A103580, A308546, A326080, A326083, A326117.

Sequence in context: A143823 A119983 A364465 * A192758 A085489 A101268

Adjacent sequences: A151894 A151895 A151896 * A151898 A151899 A151900

Keyword

nonn

Author

David Wasserman, Apr 16 2008

Extensions

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

Status

approved