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A308251 Number of subsets of {1,...,n + 1} containing n + 1 and such that all positive  differences of distinct elements are distinct. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 15:22 EDT 2021. Contains 348042 sequences. (Running on oeis4.)