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

Author

Gus Wiseman, Jul 30 2023

Keywords

• nonn

Examples

			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}
		

Links

• Rémy Sigrist, C++ program

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.

Programs

Mathematica

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

Extensions

More terms from Rémy Sigrist, Aug 06 2023