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A121269
Number of maximal sum-free subsets of {1,2,...,n}.
9
1, 1, 2, 2, 4, 5, 6, 8, 13, 17, 23, 29, 37, 51, 66, 86, 118, 158, 201, 265, 359, 471, 598, 797, 1043, 1378, 1765, 2311, 3064, 3970, 5017, 6537, 8547, 11020, 14007, 18026, 23404, 30026, 37989, 48945, 62759, 80256, 101070, 129193, 164835, 209279, 262693, 334127
OFFSET
0,3
COMMENTS
Also the number of maximal subsets of {1..n} containing no differences of pairs of elements. - Gus Wiseman, Jul 10 2019
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..80
N. Hindman and H. Jordan, Measures of sum-free intersecting families, New York J. Math. 13 (2007), 97-106.
EXAMPLE
a(5)=5 because the maximal sum-free subsets of {1,2,3,4,5} are {1,4}, {2,3}, {2,5}, {1,3,5} and {3,4,5}
From Gus Wiseman, Jul 10 2019: (Start)
The a(1) = 1 through a(8) = 13 subsets:
{1} {1} {1,3} {1,3} {1,4} {2,3} {1,4,6} {1,3,8}
{2} {2,3} {1,4} {2,3} {1,3,5} {1,4,7} {1,4,6}
{2,3} {2,5} {1,4,6} {2,3,7} {1,4,7}
{3,4} {1,3,5} {2,5,6} {2,5,6} {1,5,8}
{3,4,5} {3,4,5} {2,6,7} {1,6,8}
{4,5,6} {3,4,5} {2,5,6}
{1,3,5,7} {2,5,8}
{4,5,6,7} {2,6,7}
{3,4,5}
{1,3,5,7}
{2,3,7,8}
{4,5,6,7}
{5,6,7,8}
(End)
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Plus@@@Tuples[#, 2]]=={}&]]], {n, 0, 10}] (* Gus Wiseman, Jul 10 2019 *)
CROSSREFS
Maximal product-free subsets are A326496.
Sum-free subsets are A007865.
Maximal sum-free and product-free subsets are A326497.
Subsets with sums are A326083.
Maximal subsets without sums of distinct elements are A326498.
Sequence in context: A238687 A238433 A238424 * A211860 A250114 A056219
KEYWORD
nonn
AUTHOR
N. Hindman (nhindman(AT)aol.com), Aug 23 2006
EXTENSIONS
a(0) = 1 prepended by Gus Wiseman, Jul 10 2019
Terms a(42) and beyond from Fausto A. C. Cariboni, Oct 26 2020
STATUS
approved