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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.
4
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 17 2019
STATUS
approved