A212149 -id:A212149 - cp's OEIS frontend

A212140 Number of k-element subsets S of {1,...,n} such that mean(S) is not equal to median(S).

0, 0, 0, 2, 8, 26, 68, 164, 370, 806, 1706, 3554, 7312, 14930, 30312, 61318, 123700, 249096, 500912, 1006316

Offset: 1

Clark Kimberling, May 06 2012

nonn

Row sums of the triangular array at A212148.

t[n_, k_] := t[n, k] = Count[Map[Median[#] == 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}]
Table[s[n], {n, 1, 20}] (* A212140 *)
%/2                     (* A212149 *)
(* Peter J. C. Moses, May 01 2012 *)

A212148 Triangular array: T(n,k) is the number of k-element subsets S of {1,...,n} such that mean(S) is not equal to median(S).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 14, 8, 4, 0, 0, 0, 26, 22, 16, 4, 0, 0, 0, 44, 48, 46, 20, 6, 0, 0, 0, 68, 92, 108, 66, 30, 6, 0, 0, 0, 100, 160, 222, 174, 106, 36, 8, 0, 0, 0, 140, 260, 414, 396, 298, 142, 48, 8, 0, 0, 0, 190, 400, 720, 810, 728, 440

Offset: 1

Clark Kimberling, May 06 2012

Row sums: A212140.

			First 7 rows:
0
0...0
0...0...0
0...0...2....0
0...0...6....2....0
0...0...14...8....4...0
0...0...26...22...16...4...0
The subsets counted by T(5,3) are {1,2,4}, {1,2,5}, {1,3,4}, {1,4,5}, {2,3,5}, {2,4,5}.

Cf. A212139.

t[n_, k_] := t[n, k] = Count[Map[Median[#] == 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}]
Table[s[n], {n, 1, 20}] (* A212140 *)
%/2                     (* A212149 *)
(* Peter J. C. Moses, May 01 2012 *)

cp's OEIS Frontend

A212140 Number of k-element subsets S of {1,...,n} such that mean(S) is not equal to median(S).

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