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A325879 Number of maximal subsets of {1..n} such that every ordered pair of distinct elements has a different difference. 11
1, 1, 1, 3, 3, 6, 14, 20, 24, 36, 64, 110, 176, 238, 294, 370, 504, 736, 1086, 1592, 2240 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..20.

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.

Cf. A002033, A108917, A143824, A196723.

Cf. A325859, A325861, A325865, A325867, A325869, A325878, A325992.

Sequence in context: A123289 A096572 A318540 * A325865 A110523 A145597

Adjacent sequences:  A325876 A325877 A325878 * A325880 A325881 A325882

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 02 2019

STATUS

approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)