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A212137 Triangular array:  T(n,k) is the number of k-element subsets of {1,...,n} whose average is not an integer. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A252729 A121552 A158118 * A230295 A147592 A108885

Adjacent sequences:  A212134 A212135 A212136 * A212138 A212139 A212140

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, May 06 2012

STATUS

approved

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Last modified February 26 08:33 EST 2020. Contains 332277 sequences. (Running on oeis4.)