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A212138 Triangular array:  T(n,k) is the number of k-element subsets S of {1,...,n} whose average is in S. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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: A088673 A236138 A035614 * A133735 A238801 A095704

Adjacent sequences:  A212135 A212136 A212137 * A212139 A212140 A212141

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, May 06 2012

STATUS

approved

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Last modified July 13 12:30 EDT 2020. Contains 335687 sequences. (Running on oeis4.)