A212147 a(n) = (A212146(n)-1)/2.

0, 1, 3, 6, 11, 18, 29, 45, 70, 108, 170, 270, 439, 726, 1227, 2108, 3685, 6523, 11687, 21129, 38513, 70649, 130347, 241610, 449735, 840134, 1574537, 2959350, 5576730, 10533846, 19940812, 37823859, 71878024, 136827410, 260884686, 498167480, 952607343

Offset: 1

Author

Clark Kimberling, May 06 2012

Keywords

• nonn

Comments

A212146(n) is the number of subsets of {1,...,n} having mean=median.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A212138.

Programs

Mathematica

t[n_, k_] := t[n, k] = Count[Map[Median[#] == Mean[#] &, Subsets[Range[n], {k}]], True]
Flatten[Table[t[n, k], {n, 1, 12}, {k, 1, n}]]  (* A212139 *)
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, 22}]   (* A212146 *)
(% - 1)/2                 (* A212147 *)
(* Peter J. C. Moses, May 01 2012 *)

Extensions

a(23)-a(37) from Hiroaki Yamanouchi, Oct 03 2014