A364465 Number of subsets of {1..n} with all different first differences of elements.

1, 2, 4, 7, 13, 22, 36, 61, 99, 156, 240, 381, 587, 894, 1334, 1967, 2951, 4370, 6406, 9293, 13357, 18976, 27346, 39013, 55437, 78154, 109632, 152415, 210801, 293502, 406664, 561693, 772463, 1058108, 1441796, 1956293, 2639215, 3579542, 4835842, 6523207

Offset

0,2

Links

Table of n, a(n) for n=0..39.

Rémy Sigrist, C++ program

Example

The a(0) = 1 through a(4) = 13 subsets:
  {}  {}   {}     {}     {}
      {1}  {1}    {1}    {1}
           {2}    {2}    {2}
           {1,2}  {3}    {3}
                  {1,2}  {4}
                  {1,3}  {1,2}
                  {2,3}  {1,3}
                         {1,4}
                         {2,3}
                         {2,4}
                         {3,4}
                         {1,2,4}
                         {1,3,4}

Mathematica

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

Crossrefs

For all differences of pairs of elements we have A196723

For partitions instead of subsets we have A325325, strict A320347.

For subset-sums we have A325864, for partitions A108917, A275972.

A007318 counts subsets by length.

A053632 counts subsets by sum.

A363260 counts partitions disjoint from differences, complement A364467.

A364463 counts subsets disjoint from differences, complement A364466.

Cf. A000009, A008289, A011782, A236912, A320348, A325857, A325877, A325878, A326083, A364345, A364346.

Sequence in context: A325864 A143823 A119983 * A151897 A192758 A085489

Adjacent sequences: A364462 A364463 A364464 * A364466 A364467 A364468

Keyword

nonn

Author

Gus Wiseman, Jul 30 2023

Extensions

More terms from Rémy Sigrist, Aug 06 2023

Status

approved