A212137 Triangular array: T(n,k) is the number of k-element subsets of {1,...,n} whose average is not an integer.

0, 0, 1, 0, 2, 0, 0, 4, 2, 1, 0, 6, 6, 4, 0, 0, 9, 12, 11, 4, 1, 0, 12, 22, 26, 16, 6, 0, 0, 16, 36, 52, 44, 24, 6, 1, 0, 20, 54, 94, 100, 70, 30, 8, 0, 0, 25, 78, 156, 200, 176, 102, 39, 8, 1, 0, 30, 108, 246, 368, 386, 282, 144, 48, 10, 0, 0, 36, 144, 369, 632, 772, 678, 431, 194, 60, 10, 1

Offset

1,5

Comments

Alternating row sums: -1,-2,-3,-4,-5,-6,...

Let S(n,k) be the number in row n and column k of the array A061865; then S(n,k)+T(n,k)=C(n,k), for 1<=k<=n, n>=1.

Links

Alois P. Heinz, Rows n = 1..90, flattened

Example

First 7 rows:
0
0...1
0...2....0
0...4....2....1
0...6....6....4....0
0...9....12...11...4....1
0...12...22...26...16...6...0

Mathematica

t[n_, k_] := t[n, k] =
  Count[Map[IntegerQ[Mean[#]] &, Subsets[Range[n], {k}]], False]
Flatten[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]
TableForm[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]
s[n_] := Sum[t[n, k], {k, 1, n}]
(* Peter J. C. Moses, May 01 2012 *)

Crossrefs

Cf. A061865.

Sequence in context: A121552 A350785 A158118 * A346462 A230295 A147592

Adjacent sequences: A212134 A212135 A212136 * A212138 A212139 A212140

Keyword

nonn,tabl

Author

Clark Kimberling, May 06 2012

Status

approved