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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).
1
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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 06 2012
STATUS
approved