A308251 Number of subsets of {1,...,n + 1} containing n + 1 and such that all positive differences of distinct elements are distinct.

1, 2, 3, 6, 9, 14, 21, 34, 49, 76, 101, 146, 205, 294, 397, 560, 747, 1028, 1341, 1810, 2343, 3178, 4051, 5370, 6921, 9014, 11361, 14838, 18719, 24082, 29953, 38220, 47663, 60550, 74619, 93848, 115961, 145320, 177549, 221676, 270335, 335124

Offset

0,2

Comments

Also the number of subsets of {1...n} containing no positive differences of the elements and such that all such differences are distinct.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..99 (terms 0..41 from Gus Wiseman, terms 42..80 from Vaclav Kotesovec)

Formula

First differences of A143823. Partial sums of A169942.

Example

The a(0) = 1 through a(5) = 14 subsets:
  {1}  {2}    {3}    {4}      {5}      {6}
       {1,2}  {1,3}  {1,4}    {1,5}    {1,6}
              {2,3}  {2,4}    {2,5}    {2,6}
                     {3,4}    {3,5}    {3,6}
                     {1,2,4}  {4,5}    {4,6}
                     {1,3,4}  {1,2,5}  {5,6}
                              {1,4,5}  {1,2,6}
                              {2,3,5}  {1,3,6}
                              {2,4,5}  {1,4,6}
                                       {1,5,6}
                                       {2,3,6}
                                       {2,5,6}
                                       {3,4,6}
                                       {3,5,6}

Mathematica

Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&UnsameQ@@Abs[Subtract@@@Subsets[#, {2}]]&]], {n, 15}]

Crossrefs

Cf. A000079, A108917, A143823, A143824, A169942, A325676, A325677, A325683, A325687.

Sequence in context: A320595 A227564 A173303 * A058609 A333697 A128518

Adjacent sequences: A308248 A308249 A308250 * A308252 A308253 A308254

Keyword

nonn

Author

Gus Wiseman, May 17 2019

Status

approved