The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326080 Number of subsets of {1..n} containing the sum of every subset whose sum is <= n. 37
 1, 2, 4, 7, 12, 19, 31, 47, 73, 110, 168, 247, 375, 546, 817, 1193, 1769, 2552, 3791, 5445, 8012, 11517, 16899, 24144, 35391, 50427, 73614, 104984, 152656, 216802, 315689, 447473, 648813, 920163, 1332991, 1884735, 2728020, 3853437, 5568644, 7868096, 11347437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equivalently, a(n) is the number of subsets of {1..n} containing the sum of any two distinct elements whose sum is <= n. The summands must be distinct. The case where they are allowed to be equal is A326083. If A151897 counts sum-free sets, this sequence counts sum-closed sets. This is different from sum-full sets (A093971). LINKS Table of n, a(n) for n=0..40. EXAMPLE The a(0) = 1 through a(5) = 19 subsets: {} {} {} {} {} {} {1} {1} {1} {1} {1} {2} {2} {2} {2} {1,2} {3} {3} {3} {1,3} {4} {4} {2,3} {1,4} {5} {1,2,3} {2,3} {1,5} {2,4} {2,4} {3,4} {2,5} {1,3,4} {3,4} {2,3,4} {3,5} {1,2,3,4} {4,5} {1,4,5} {2,3,5} {2,4,5} {3,4,5} {1,3,4,5} {2,3,4,5} {1,2,3,4,5} The a(6) = 31 subsets: {} {1} {1,6} {1,5,6} {1,4,5,6} {1,3,4,5,6} {1,2,3,4,5,6} {2} {2,5} {2,3,5} {2,3,5,6} {2,3,4,5,6} {3} {2,6} {2,4,6} {2,4,5,6} {4} {3,4} {2,5,6} {3,4,5,6} {5} {3,5} {3,4,5} {6} {3,6} {3,4,6} {4,5} {3,5,6} {4,6} {4,5,6} {5,6} MATHEMATICA Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Plus@@@Subsets[#, {2}], #<=n&]]&]], {n, 0, 10}] PROG (PARI) a(n)={ my(recurse(k, b)= if( k > n, 1, my(t=self()(k + 1, b + (1<

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 4 15:30 EDT 2023. Contains 365885 sequences. (Running on oeis4.)