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

1,2

Links

Table of n, a(n) for n=1..84.

Example

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}.

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 *)

Crossrefs

Cf. A061865.

Sequence in context: A361755 A362755 A035614 * A133735 A238801 A095704

Adjacent sequences: A212135 A212136 A212137 * A212139 A212140 A212141

Keyword

nonn,tabl

Author

Clark Kimberling, May 06 2012

Status

approved