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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

%I

%S 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,

%T 36,52,44,24,6,1,0,20,54,94,100,70,30,8,0,0,25,78,156,200,176,102,39,

%U 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

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

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

%C 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.

%H Alois P. Heinz, <a href="/A212137/b212137.txt">Rows n = 1..90, flattened</a>

%e First 7 rows:

%e 0

%e 0...1

%e 0...2....0

%e 0...4....2....1

%e 0...6....6....4....0

%e 0...9....12...11...4....1

%e 0...12...22...26...16...6...0

%t t[n_, k_] := t[n, k] =

%t Count[Map[IntegerQ[Mean[#]] &, Subsets[Range[n], {k}]], False]

%t Flatten[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]

%t TableForm[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]

%t s[n_] := Sum[t[n, k], {k, 1, n}]

%t (* _Peter J. C. Moses_, May 01 2012 *)

%Y Cf. A061865.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, May 06 2012

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Last modified April 3 12:37 EDT 2020. Contains 333197 sequences. (Running on oeis4.)