A212138 Triangular array: T(n,k) is the number of k-element subsets S of {1,...,n} whose average is in S.

1, 2, 0, 3, 0, 1, 4, 0, 2, 0, 5, 0, 4, 0, 1, 6, 0, 6, 2, 2, 0, 7, 0, 9, 4, 5, 0, 1, 8, 0, 12, 8, 10, 2, 2, 0, 9, 0, 16, 14, 18, 8, 6, 0, 1, 10, 0, 20, 22, 32, 20, 14, 4, 2, 0, 11, 0, 25, 32, 52, 42, 34, 14, 7, 0, 1, 12, 0, 30, 46, 80, 80, 72, 42, 22, 4, 2, 0, 13, 0, 36, 62, 119, 1

Offset: 1

Author

Clark Kimberling, May 06 2012

Keywords

• nonn
• tabl

Examples

			First 7 rows:
  1
  2...0
  3...0...1
  4...0...2...0
  5...0...4...0...1
  6...0...6...2...2...0
  7...0...9...4...5...0...1
T(5,3) counts these subsets: {1,2,3}, {1,3,5}, {2,3,4}, {3,4,5}.
		

Crossrefs

Cf. A061865.

Programs

Mathematica

t[n_, k_] := Length[Flatten[Map[Apply[Intersection, #] &,
    Select[Map[{#, {Mean[#]}} &, Subsets[Range[n], {k}]], IntegerQ[Last[Last[#]]] &]]]]
Flatten[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]
TableForm[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]
(* Peter J. C. Moses, May 01 2012 *)