A212146 Number of subsets of {1,...,n} having mean=median.

1, 3, 7, 13, 23, 37, 59, 91, 141, 217, 341, 541, 879, 1453, 2455, 4217, 7371, 13047, 23375, 42259, 77027, 141299, 260695, 483221, 899471, 1680269, 3149075, 5918701, 11153461, 21067693, 39881625, 75647719, 143756049, 273654821, 521769373, 996334961, 1905214687

Offset: 1

Author

Clark Kimberling, May 06 2012

Keywords

• nonn

Comments

a(n) = sum of terms of row n of the triangle A212139.

a(n) = 1+2*A212147(n).

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) from Alois P. Heinz, Feb 12 2014

a(24)-a(37) from Hiroaki Yamanouchi, Oct 03 2014