A212138 - OEIS

%I #13 Oct 27 2024 03:10:44

%S 1,2,0,3,0,1,4,0,2,0,5,0,4,0,1,6,0,6,2,2,0,7,0,9,4,5,0,1,8,0,12,8,10,

%T 2,2,0,9,0,16,14,18,8,6,0,1,10,0,20,22,32,20,14,4,2,0,11,0,25,32,52,

%U 42,34,14,7,0,1,12,0,30,46,80,80,72,42,22,4,2,0,13,0,36,62,119,1

%N Triangular array:  T(n,k) is the number of k-element subsets S of {1,...,n} whose average is in S.

%e First 7 rows:

%e   1

%e   2...0

%e   3...0...1

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

%e   5...0...4...0...1

%e   6...0...6...2...2...0

%e   7...0...9...4...5...0...1

%e T(5,3) counts these subsets: {1,2,3}, {1,3,5}, {2,3,4}, {3,4,5}.

%t t[n_, k_] := Length[Flatten[Map[Apply[Intersection, #] &,

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

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

%Y Cf. A061865.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, May 06 2012