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A325879
Number of maximal subsets of {1..n} such that every ordered pair of distinct elements has a different difference.
12
1, 1, 1, 3, 3, 6, 14, 20, 24, 36, 64, 110, 176, 238, 294, 370, 504, 736, 1086, 1592, 2240, 2982, 3788, 4700, 5814, 7322, 9396, 12336, 16552, 22192, 29310, 38046, 48368, 60078, 73722, 89416, 108208, 131310, 160624, 198002, 247408, 310410, 390924, 490818, 613344, 758518
OFFSET
0,4
COMMENTS
Also the number of maximal subsets of {1..n} such that every orderless pair of (not necessarily distinct) elements has a different sum.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..100
EXAMPLE
The a(0) = 1 through a(7) = 20 subsets:
{} {1} {1,2} {1,2} {2,3} {1,2,4} {1,2,4} {1,2,4}
{1,3} {1,2,4} {1,2,5} {1,2,5} {1,2,6}
{2,3} {1,3,4} {1,3,4} {1,2,6} {1,3,4}
{1,4,5} {1,3,4} {1,4,5}
{2,3,5} {1,3,6} {1,4,6}
{2,4,5} {1,4,5} {1,5,6}
{1,4,6} {2,3,5}
{1,5,6} {2,3,6}
{2,3,5} {2,3,7}
{2,3,6} {2,4,5}
{2,4,5} {2,4,7}
{2,5,6} {2,5,6}
{3,4,6} {2,6,7}
{3,5,6} {3,4,6}
{3,4,7}
{3,5,6}
{4,5,7}
{4,6,7}
{1,2,5,7}
{1,3,6,7}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Subtract@@@Subsets[Union[#], {2}]&]]], {n, 0, 10}]
CROSSREFS
The subset case is A143823.
The maximal case is A325879.
The integer partition case is A325858.
The strict integer partition case is A325876.
Heinz numbers of the counterexamples are given by A325992.
Sequence in context: A123289 A096572 A318540 * A325865 A110523 A145597
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
EXTENSIONS
a(21)-a(45) from Fausto A. C. Cariboni, Feb 08 2022
STATUS
approved