A364671 Number of subsets of {1..n} containing all of their own first differences.

1, 2, 4, 6, 10, 14, 23, 34, 58, 96, 171, 302, 565, 1041, 1969, 3719, 7105, 13544, 25999, 49852, 95949, 184658, 356129, 687068, 1327540, 2566295, 4966449, 9617306, 18640098, 36150918, 70166056, 136272548, 264844111, 515036040, 1002211421, 1951345157, 3801569113

Offset: 0

Author

Gus Wiseman, Aug 04 2023

Keywords

• nonn

Examples

			The subset {1,2,4,5,10,14} has differences (1,2,1,5,4) so is counted under a(14).
The a(0) = 1 through a(5) = 14 subsets:
  {}  {}   {}     {}       {}         {}
      {1}  {1}    {1}      {1}        {1}
           {2}    {2}      {2}        {2}
           {1,2}  {3}      {3}        {3}
                  {1,2}    {4}        {4}
                  {1,2,3}  {1,2}      {5}
                           {2,4}      {1,2}
                           {1,2,3}    {2,4}
                           {1,2,4}    {1,2,3}
                           {1,2,3,4}  {1,2,4}
                                      {1,2,3,4}
                                      {1,2,3,5}
                                      {1,2,4,5}
                                      {1,2,3,4,5}
		

Links

• Rémy Sigrist, C++ program

Crossrefs

For differences of all strict pairs we have A054519, for partitions A007862.

For "disjoint" instead of "subset" we have A364463, partitions A363260.

For "non-disjoint" we have A364466, partitions A364467 (strict A364536).

The complement is counted by A364672, partitions A364673, A364674, A364675.

First differences of terms are A364752, complement A364753.

Cf. A151897, A196723, A237667, A237668, A325325, A326083, A363225, A364345, A364464, A364537.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]], SubsetQ[#,Differences[#]]&]], {n,0,10}]

Extensions

More terms from Rémy Sigrist, Aug 06 2023