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

0,2

Links

Table of n, a(n) for n=0..36.

Rémy Sigrist, C++ program

Example

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}

Mathematica

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

Prog

(C++) See Links section.

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.

Sequence in context: A239951 A077625 A027383 * A280611 A138016 A239787

Adjacent sequences: A364668 A364669 A364670 * A364672 A364673 A364674

Keyword

nonn

Author

Gus Wiseman, Aug 04 2023

Extensions

More terms from Rémy Sigrist, Aug 06 2023

Status

approved