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

0,3

Links

Table of n, a(n) for n=0..37.

Rémy Sigrist, C++ program

Example

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}

Mathematica

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

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.

Sequence in context: A358429 A222736 A053656 * A035054 A099537 A109525

Adjacent sequences: A364749 A364750 A364751 * A364753 A364754 A364755

Keyword

nonn

Author

Gus Wiseman, Aug 06 2023

Extensions

More terms from Rémy Sigrist, Aug 06 2023

Status

approved