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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.

%I A212137 #17 Feb 12 2014 22:04:31
%S A212137 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 A212137 36,52,44,24,6,1,0,20,54,94,100,70,30,8,0,0,25,78,156,200,176,102,39,
%U A212137 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 A212137 Triangular array:  T(n,k) is the number of k-element subsets of {1,...,n} whose average is not an integer.
%C A212137 Alternating row sums:  -1,-2,-3,-4,-5,-6,...
%C A212137 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 A212137 Alois P. Heinz, <a href="/A212137/b212137.txt">Rows n = 1..90, flattened</a>
%e A212137 First 7 rows:
%e A212137 0
%e A212137 0...1
%e A212137 0...2....0
%e A212137 0...4....2....1
%e A212137 0...6....6....4....0
%e A212137 0...9....12...11...4....1
%e A212137 0...12...22...26...16...6...0
%t A212137 t[n_, k_] := t[n, k] =
%t A212137   Count[Map[IntegerQ[Mean[#]] &, Subsets[Range[n], {k}]], False]
%t A212137 Flatten[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]
%t A212137 TableForm[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]
%t A212137 s[n_] := Sum[t[n, k], {k, 1, n}]
%t A212137 (* _Peter J. C. Moses_, May 01 2012 *)
%Y A212137 Cf. A061865.
%K A212137 nonn,tabl
%O A212137 1,5
%A A212137 _Clark Kimberling_, May 06 2012