|
|
A093971
|
|
Number of sum-full subsets of {1,...,n}; subsets A such that there is a solution to x+y=z for x,y,z in A.
|
|
75
|
|
|
0, 1, 2, 7, 16, 40, 86, 195, 404, 873, 1795, 3727, 7585, 15537, 31368, 63582, 127933, 257746, 517312, 1038993, 2081696, 4173322, 8355792, 16731799, 33484323, 67014365, 134069494, 268234688, 536562699, 1073326281, 2146849378, 4294117419, 8588623348, 17178130162
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
In sumset notation, number of subsets A of {1,...,n} such that the intersection of A and 2A is nonempty.
A variation of binary sum-full sets where parts can be re-used, this sequence counts subsets of {1..n} containing a part equal to the sum of two other (possibly equal) parts. The complement is counted by A007865. The non-binary version is A364914. For non-re-usable parts we have A088809. - Gus Wiseman, Aug 14 2023
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(1) = 0 through a(5) = 16 subsets:
. {1,2} {1,2} {1,2} {1,2}
{1,2,3} {2,4} {2,4}
{1,2,3} {1,2,3}
{1,2,4} {1,2,4}
{1,3,4} {1,2,5}
{2,3,4} {1,3,4}
{1,2,3,4} {1,4,5}
{2,3,4}
{2,3,5}
{2,4,5}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
|
|
MATHEMATICA
|
Table[Length[Select[Subsets[Range[n]], Intersection[#, Total/@Tuples[#, 2]]!={}&]], {n, 0, 10}] (* Gus Wiseman, Aug 14 2023 *)
|
|
CROSSREFS
|
The complement is counted by A007865.
The non-binary version w/o re-usable parts is A364534, complement A151897.
The version for partitions is A363225:
- non-binary without re-usable parts A237668.
The complement for partitions is A364345:
- non-binary without re-usable parts A237667.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|