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A325866
Number of subsets of {1..n} containing n such that every subset has a different sum.
5
1, 2, 3, 6, 9, 14, 20, 35, 44, 76, 96, 139, 179, 257, 312, 483, 561, 793, 970, 1459, 1535, 2307, 2619, 3503, 4130, 5478, 5973, 8165, 9081, 11666, 13176, 17738, 18440, 24778, 26873, 35187, 38070, 49978, 51776, 72457, 74207, 92512, 102210, 135571, 136786, 179604
OFFSET
1,2
COMMENTS
These are strict knapsack partitions (A275972) organized by maximum rather than sum.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 1..150
EXAMPLE
The a(1) = 1 through a(6) = 14 subsets:
{1} {2} {3} {4} {5} {6}
{1,2} {1,3} {1,4} {1,5} {1,6}
{2,3} {2,4} {2,5} {2,6}
{3,4} {3,5} {3,6}
{1,2,4} {4,5} {4,6}
{2,3,4} {1,2,5} {5,6}
{1,3,5} {1,2,6}
{2,4,5} {1,3,6}
{3,4,5} {1,4,6}
{2,3,6}
{2,5,6}
{3,4,6}
{3,5,6}
{4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&UnsameQ@@Plus@@@Subsets[#]&]], {n, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 01 2019
EXTENSIONS
a(18)-a(46) from Alois P. Heinz, Jun 03 2019
STATUS
approved