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

Author

Clark Kimberling, May 06 2012

Keywords

• nonn
• tabl

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A061865.

Programs

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 *)