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A151897
Number of subsets of {1, 2, ..., n} such that no member is a sum of distinct other members.
70
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 *)
KEYWORD
nonn
AUTHOR
David Wasserman, Apr 16 2008
EXTENSIONS
a(0) = 1 prepended by Gus Wiseman, Jun 07 2019
STATUS
approved