A364752 Number of subsets of {1..n} containing n and all first differences.

1, 1, 2, 2, 4, 4, 9, 11, 24, 38, 75, 131, 263, 476, 928, 1750, 3386, 6439, 12455, 23853, 46097, 88709, 171471, 330939, 640472, 1238755, 2400154, 4650857, 9022792, 17510820, 34015138, 66106492, 128571563, 250191929, 487175381, 949133736, 1850223956, 3608650389

Offset: 0

Author

Gus Wiseman, Aug 06 2023

Keywords

• nonn

Examples

			The a(1) = 1 through a(6) = 9 subsets:
  {1}  {2}    {3}      {4}        {5}          {6}
       {1,2}  {1,2,3}  {2,4}      {1,2,3,5}    {3,6}
                       {1,2,4}    {1,2,4,5}    {2,4,6}
                       {1,2,3,4}  {1,2,3,4,5}  {1,2,3,6}
                                               {1,2,4,6}
                                               {1,2,3,4,6}
                                               {1,2,3,5,6}
                                               {1,2,4,5,6}
                                               {1,2,3,4,5,6}
		

Links

• Rémy Sigrist, C++ program

Crossrefs

Partial sums are A364671, complement A364672.

The complement is counted by A364753.

A054519 counts subsets containing differences, A326083 containing sums.

A364463 counts subsets disjoint from differences, complement A364466.

A364673 counts partitions containing differences, A364674, A364675.

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

Programs

Mathematica

Table[If[n==0,1,Length[Select[Subsets[Range[n]], MemberQ[#,n]&&SubsetQ[#,Differences[#]]&]]],{n,0,10}]

Extensions

More terms from Rémy Sigrist, Aug 06 2023