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).

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

1,9

Comments

Row sums: A212140.

Links

Table of n, a(n) for n=1..74.

Example

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}.

Mathematica

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 *)

Crossrefs

Cf. A212139.

Sequence in context: A158360 A309746 A094315 * A364988 A358622 A336563

Adjacent sequences: A212145 A212146 A212147 * A212149 A212150 A212151

Keyword

nonn,tabl

Author

Clark Kimberling, May 06 2012

Status

approved