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

Author

Gus Wiseman, May 17 2019

Keywords

• nonn

Comments

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

Examples

			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}
		

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)

Crossrefs

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

Programs

Mathematica

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

Formula

First differences of A143823. Partial sums of A169942.