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

1,2

Comments

Row sums: A212146.

Links

Table of n, a(n) for n=1..78.

Example

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}.

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}]]
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 *)

Crossrefs

Cf. A212138.

Sequence in context: A073020 A090349 A157379 * A093430 A074659 A131251

Adjacent sequences: A212136 A212137 A212138 * A212140 A212141 A212142

Keyword

nonn,tabl

Author

Clark Kimberling, May 06 2012

Status

approved