A212140 -id:A212140 - cp's OEIS frontend

A212149 Number of k-element subsets S of {1,...,n} such that mean(S)

0, 0, 0, 1, 4, 13, 34, 82, 185, 403, 853, 1777, 3656, 7465, 15156, 30659, 61850, 124548, 250456, 503158

Offset: 1

Clark Kimberling, May 06 2012

nonn

Also the number of k-element subsets S of {1,...,n} such that mean(S)>median(S). A212149(n) = A212140(n)/2.

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

A212149 Number of k-element subsets S of {1,...,n} such that mean(S)

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