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A326495
Number of subsets of {1..n} containing no sums or products of pairs of elements.
9
1, 1, 2, 4, 6, 11, 17, 30, 45, 71, 101, 171, 258, 427, 606, 988, 1328, 2141, 3116, 4952, 6955, 11031, 15320, 23978, 33379, 48698, 66848, 104852, 144711, 220757, 304132, 461579, 636555, 973842, 1316512, 1958827, 2585432, 3882842, 5237092, 7884276, 10555738, 15729292
OFFSET
0,3
COMMENTS
The pairs are not required to be strict.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..90
FORMULA
For n > 0, a(n) = A326490(n) - 1.
EXAMPLE
The a(1) = 1 through a(6) = 17 subsets:
{} {} {} {} {} {}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{2,3} {4} {4} {4}
{2,3} {5} {5}
{3,4} {2,3} {6}
{2,5} {2,3}
{3,4} {2,5}
{3,5} {2,6}
{4,5} {3,4}
{3,4,5} {3,5}
{4,5}
{4,6}
{5,6}
{2,5,6}
{3,4,5}
{4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], Intersection[#, Union[Plus@@@Tuples[#, 2], Times@@@Tuples[#, 2]]]=={}&]], {n, 0, 10}]
CROSSREFS
Subsets without sums are A007865.
Subsets without products are A326489.
Subsets without differences or quotients are A326490.
Maximal subsets without sums or products are A326497.
Subsets with sums (and products) are A326083.
Sequence in context: A004698 A014217 A034297 * A026636 A026658 A138688
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2019
EXTENSIONS
a(19)-a(41) from Andrew Howroyd, Aug 25 2019
STATUS
approved