A212146 -id:A212146 - cp's OEIS frontend

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

Clark Kimberling, May 06 2012

nonn

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

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

Cf. A212138.

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 *)

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

A212139 Triangular array: T(n,k) is the number of k-element subsets of {1,...,n} that satisfy mean=median.

Original entry on oeis.org

1, 2, 1, 3, 3, 1, 4, 6, 2, 1, 5, 10, 4, 3, 1, 6, 15, 6, 7, 2, 1, 7, 21, 9, 13, 5, 3, 1, 8, 28, 12, 22, 10, 8, 2, 1, 9, 36, 16, 34, 18, 18, 6, 3, 1, 10, 45, 20, 50, 30, 36, 14, 9, 2, 1, 11, 55, 25, 70, 48, 66, 32, 23, 7, 3, 1, 12, 66, 30, 95, 72, 114, 64, 55, 20, 10, 2, 1

Offset: 1

Clark Kimberling, May 06 2012

Row sums: A212146.

			First 7 rows:
  1
  2...1
  3...3....1
  4...6....2...1
  5...10...4...3....1
  6...15...6...7....2...1
  7...21...9...13...5...3...1
T(5,3) counts these subsets: {1,2,3}, {1,3,5}, {2,3,4}, {3,4,5}.

Cf. A212138.

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}]]
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 *)

cp's OEIS Frontend

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

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