A212352 Row sums of A047997.

0, 1, 3, 9, 25, 75, 235, 759, 2521, 8555, 29503, 103129, 364547, 1300819, 4679471, 16952161, 61790441, 226451035, 833918839, 3084255127, 11451630043, 42669225171, 159497648599, 597950875255, 2247724108771, 8470205600639

Offset: 0

Author

N. J. A. Sloane, May 16 2012

Keywords

• nonn

Comments

Also the number of nonempty subsets of {1..2n} with mean n, even bisection of A362046. - Gus Wiseman, Apr 15 2023

Examples

			From _Gus Wiseman_, Apr 15 2023: (Start)
The a(1) = 1 through a(3) = 9 subsets:
  {1}  {2}      {3}
       {1,3}    {1,5}
       {1,2,3}  {2,4}
                {1,2,6}
                {1,3,5}
                {2,3,4}
                {1,2,3,6}
                {1,2,4,5}
                {1,2,3,4,5}
(End)
		

Crossrefs

Equals A047653(n) - 1.

Row sums of A047997.

For median instead of mean we have A079309, bisection of A361801.

Even bisection of A362046, zero-based version A070925.

A000980 counts nonempty subsets of {1..2n-1} with mean n.

A007318 counts subsets by length.

A327475 counts subsets with integer mean.

A327481 counts subsets by mean.

Cf. A000975, A013580, A024718, A057552, A133406, A361866.

Programs

Mathematica

Table[Length[Select[Subsets[Range[2n]],Mean[#]==n&]],{n,0,6}] (* Gus Wiseman, Apr 15 2023 *)

Formula

From Gus Wiseman, Apr 15 2023: (Start)

a(n) = A000980(n)/2 - 1.

a(n) = A047653(n) - 1.

a(n) = A133406(2n+1) - 1.

a(n) = A362046(2n).

(End)