A212138 -id:A212138 - cp's OEIS frontend

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

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 *)

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

Original entry on oeis.org

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

Clark Kimberling, May 06 2012

nonn

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

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

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) from Alois P. Heinz, Feb 12 2014

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

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

Original entry on oeis.org

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

cp's OEIS Frontend

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

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

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

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