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A212149
Number of k-element subsets S of {1,...,n} such that mean(S)<median(S).
3
0, 0, 0, 1, 4, 13, 34, 82, 185, 403, 853, 1777, 3656, 7465, 15156, 30659, 61850, 124548, 250456, 503158
OFFSET
1,5
COMMENTS
Also the number of k-element subsets S of {1,...,n} such that mean(S)>median(S). A212149(n) = A212140(n)/2.
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
Sequence in context: A029860 A262200 A213578 * A357284 A208740 A372768
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 06 2012
STATUS
approved